THEMES AND CAPSTONE UNITS
18: Global economy
19: Inequality
20: Environment
21: Innovation
22: Politics and policy
UNIT 4
SOCIAL INTERACTIONS
A COMBINATION OF SELF-INTEREST, A REGARD
FOR THE WELLBEING OF OTHERS, AND
APPROPRIATE INSTITUTIONS CAN YIELD
DESIRABLE SOCIAL OUTCOMES WHEN PEOPLE
INTERACT
• Game theory is a way of understanding how people interact based
on the constraints that limit their actions, their motives, and their
beliefs about what others will do.
• Experiments and other evidence show that self-interest, a concern for
others, and a preference for fairness are all important motives that
explain how people interact.
• In most interactions there is some conflict of interest between people,
but also some opportunity for mutual gain.
• The pursuit of self-interest can sometimes lead to results that are con-
sidered good by all participants, or outcomes that none of the
participants would prefer.
• Self-interest can be harnessed for the general good in markets, by gov-
ernments limiting the actions that people are free to take, and by one’s
peers imposing punishments on actions that lead to bad outcomes.
• A concern for others and for fairness allows us to internalize the effects
of our actions on others, and so can contribute to good social outcomes.
This is the blunt beginning of the executive summary of the Stern Review,
published in 2006. The British Chancellor of the Exchequer (finance
minister) commissioned a group of economists, led by former World Bank
chief economist Sir Nicholas (now Lord) Stern, to assess the evidence for
climate change, and to try to understand its economic implications. The
Nicholas Stern. 2007. The Eco-
nomics of Climate Change: The
Stern Review. Cambridge:
Cambridge University Press. Read
the executive summary
(https://tinyco.re/5785938).
The scientific evidence is now overwhelming: climate change
presents very serious global risks, and it demands an urgent global
response.
Paul Cézanne’s Les Joueurs de Carte (Card Players)
131
social dilemma A situation in
which actions taken independently
by individuals in pursuit of their
own private objectives result in an
outcome which is inferior to some
other feasible outcome that could
have occurred if people had acted
together, rather than as individuals.
free ride Benefiting from the
contributions of others to some
cooperative project without
contributing oneself.
Stern Review predicts that the benefits of early action to slow climate
change will outweigh the costs of neglecting the issue.
The Fifth Assessment Report by the Intergovernmental Panel on
Climate Change (IPCC) agrees. Early action would mean a significant cut in
greenhouse gas emissions, by reducing our consumption of energy-
intensive goods, a switch to different energy technologies, reducing the
impacts of agriculture and land-use change, and an improvement in the
efficiency of current technologies.
But none of this will happen if we pursue what Stern referred to as ‘busi-
ness as usual’: a scenario in which people, governments and businesses are
free to pursue their own pleasures, politics, and profits without taking
adequate account of the effect of their actions on others, including future
generations.
National governments disagree on the policies that should be adopted.
Many nations in the developed world are pressing for strict global controls
on carbon emissions, while others, whose economic catch-up has until
recently been dependent on coal-burning technologies, have resisted these
measures.
The problem of climate change is far from unique. It is an example of
what is called a social dilemma. Social dilemmas—like climate change—
occur when people do not take adequate account of the effects of their
decisions on others, whether these are positive or negative.
Social dilemmas occur frequently in our lives. Traffic jams happen when
our choice of a way to get around—for example driving alone to work
rather than car-pooling—does not take account of the contribution to
congestion that we make. Similarly, overusing antibiotics for minor
illnesses may help the sick person who takes them recover more quickly,
but creates antibiotic-resistant bacteria that have a much more harmful
effect on many others.
The Tragedy of the Commons
In 1968, Garrett Hardin, a biologist, published an article about social
dilemmas in the journal Science, called ‘The Tragedy of the Commons’. He
argued that resources that are not owned by anyone (sometimes called
‘common property’ or ‘common-pool resources’) such as the earth’s
atmosphere or fish stocks, are easily overexploited unless we control access in
some way. Fishermen as a group would be better off not catching as much
tuna, and consumers as a whole would be better off not eating too much of it.
Humanity would be better off by emitting less pollutants, but if you, as an
individual, decide to cut your consumption, your carbon footprint or the
number of tuna you catch will hardly affect the global levels.
Examples of Hardin’s tragedies and other social dilemmas are all around
us: if you live with roommates, or in a family, you know just how difficult it
is to keep a clean kitchen or bathroom. When one person cleans, everyone
benefits, but it is hard work. Whoever cleans up bears this cost. The others
are sometimes called free riders. If as a student you have ever done a group
assignment, you understand that the cost of effort (to study the problem,
gather evidence, or write up the results) is individual, yet the benefits (a
better grade, higher class standing, or simply the admiration of classmates)
go to the whole group.
IPCC. 2014. ‘Climate Change 2014:
Synthesis Report’. Contribution of
Working Groups I, II and III to the
Fifth Assessment Report of the
Intergovernmental Panel on
Climate Change. Geneva,
Switzerland: IPCC.
Garrett Hardin. 1968. ‘The Tragedy
of the Commons’. Science 162
(3859): pp. 1243–1248.
Elinor Ostrom. 2008. ‘The
Challenge of Common-Pool
Resources’. Environment: Science
and Policy for Sustainable
Development 50 (4): pp. 8–21.
UNIT 4 SOCIAL INTERACTIONS
132
altruism The willingness to bear a
cost in order to benefit somebody
else.
game theory A branch of
mathematics that studies strategic
interactions, meaning situations in
which each actor knows that the
benefits they receive depend on
the actions taken by all. See also:
game.
social interactions Situations in
which the actions taken by each
person affect other people’s out-
comes as well as their own.
Resolving social dilemmas
There is nothing new about social dilemmas; we have been facing them
since prehistory.
More than 2,500 years ago, the Greek storyteller Aesop wrote about a
social dilemma in his fable Belling the Cat. A group of mice needs one of its
members to place a bell around a cat’s neck. Once the bell is on, the cat
cannot catch and eat the other mice. But the outcome may not be so good
for the mouse that takes the job. There are countless examples during wars
or natural catastrophes in which individuals sacrifice their lives for others
who are not family members, and may even be total strangers. These
actions are termed altruistic.
Altruistic self-sacrifice is not the most important way that societies
resolve social dilemmas and reduce free riding. Sometimes the problems
can be resolved by government policies. For example, governments have
successfully imposed quotas to prevent the over-exploitation of stocks of
cod in the North Atlantic. In the UK, the amount of waste that is dumped in
landfills, rather than being recycled, has been dramatically reduced by a
landfill tax.
Local communities also create institutions to regulate behaviour.
Irrigation communities need people to work to maintain the canals that
benefit the whole community. Individuals also need to use scarce water
sparingly so that other crops will flourish, although this will lead to smaller
crops for themselves. In Valencia, Spain, communities of farmers have used
a set of customary rules for centuries to regulate communal tasks and to
avoid using too much water. Since the middle ages they have had an
arbitration court called the Tribunal de las Aguas (Water Court) that resolves
conflicts between farmers about the application of the rules. The ruling of
the Tribunal is not legally enforceable. Its power comes only from the
respect of the community, yet its decisions are almost universally followed.
Even present-day global environmental problems have sometimes been
tackled effectively. The Montreal Protocol has been remarkably successful.
It was created to phase out and eventually ban the chlorofluorocarbons
(CFCs) that threatened to destroy the ozone layer that protects us against
harmful ultraviolet radiation.
In this unit, we will use the tools of game theory to model social
interactions, in which the decisions of individuals affect other people as
well as themselves. We will look at situations that result in social dilemmas
and how people can sometimes solve them—but sometimes not (or not yet),
as in the case of climate change.
But not all social interactions lead to social dilemmas, even if individuals
act in pursuit of their own interests. We will start in the next section with
an example where the ‘invisible hand’ of the market, as described by Adam
Smith, channels self-interest so that individuals acting independently do
reach a mutually beneficial outcome.
EXERCISE 4.1 SOCIAL DILEMMAS
Using the news headlines from last week:
1. Identify two social dilemmas that have been reported (try to use
examples not discussed above).
2. For each, specify how it satisfies the definition of a social dilemma.
Aesop. ‘Belling the Cat’. In Fables,
retold by Joseph Jacobs. XVII, (1).
The Harvard Classics. New York:
P. F. Collier & Son, 1909–14;
Bartleby.com, 2001.
UNIT 4 SOCIAL INTERACTIONS
133
strategic interaction A social
interaction in which the
participants are aware of the ways
that their actions affect others (and
the ways that the actions of others
affect them).
strategy An action (or a course of
action) that a person may take
when that person is aware of the
mutual dependence of the results
for herself and for others. The out-
comes depend not only on that
person’s actions, but also on the
actions of others.
game A model of strategic
interaction that describes the
players, the feasible strategies, the
information that the players have,
and their payoffs. See also: game
theory.
division of labour The
specialization of producers to carry
out different tasks in the produc-
tion process. Also known as:
specialization.
4.1 SOCIAL INTERACTIONS: GAME THEORY
On which side of the road should you drive? If you live in Japan, the UK, or
Indonesia, you drive on the left. If you live in South Korea, France, or the
US, you drive on the right. If you grew up in Sweden, you drove on the left
until 5 p.m. on 3 September 1967, and at 5.01 p.m. you started driving on
the right. The government sets a rule, and we follow it.
But suppose we just left the choice to drivers to pursue their self-interest
and to select one side of the road or the other. If everyone else was already
driving on the right, self-interest (avoiding a collision) would be sufficient
to motivate a driver to drive on the right as well. Concern for other drivers,
or a desire to obey the law, would not be necessary.
Devising policies to promote people’s wellbeing requires an under-
standing of the difference between situations in which self-interest can
promote general wellbeing, and cases in which it leads to undesirable
results. To analyse this, we will introduce game theory, a way of modelling
how people interact.
In Unit 3 we saw how a student deciding how much to study and a
farmer choosing how hard to work both faced a set of feasible options,
determined by a production function. This person then makes decisions to
obtain the best possible outcome. But in the models we have studied so far,
the outcome did not depend on what anyone else did. Neither the student
nor the farmer was engaged in a social interaction.
Social and strategic interactions
In this unit, we consider social interactions, meaning situations in which
there are two or more people, and the actions taken by each person affects
both their own outcome and other people’s outcomes. For example, one
person’s choice of how much to heat his or her home will affect everyone’s
experience of global climate change.
We use four terms:
• When people are engaged in a social interaction and are aware of the
ways that their actions affect others, and vice versa, we call this a
strategic interaction.
• A strategy is defined as an action (or a course of action) that a person
may take when that person is aware of the mutual dependence of the
results for herself and for others. The outcomes depend not only on that
person’s actions, but also on the actions of others.
• Models of strategic interactions are described as games.
• Game theory is a set of models of strategic interactions. It is widely used
in economics and elsewhere in the social sciences.
To see how game theory can clarify strategic interactions, imagine two
farmers, who we will call Anil and Bala. They face a problem: should they
grow rice or cassava? We assume that they have the ability to grow both
types of crop, but can only grow one type at a time.
Anil’s land is better suited for growing cassava, while Bala’s is better
suited for rice. The two farmers have to determine the division of labour,
that is, who will specialize in which crop. They decide this independently,
which means they do not meet together to discuss a course of action.
(Assuming independence may seem odd in this model of just two farm-
ers, but later we apply the same logic to situations like climate change, in
which hundreds or even millions of people interact, most of them total
UNIT 4 SOCIAL INTERACTIONS
134
GAME
A description of a social
interaction, which specifies:
• The players: Who is interacting
with whom
• The feasible strategies: Which
actions are open to the players
• The information: What each
player knows when making
their decision
• The payoffs: What the outcomes
will be for each of the possible
combinations of actions
strangers to one another. So assuming that Anil and Bala do not come to
some common agreement before taking action is useful for us.)
They both sell whatever crop they produce in a nearby village market.
On market day, if they bring less rice to the market, the price will be higher.
The same goes for cassava. Figure 4.1 describes their interaction, which is
what we call a game. Let’s explain what Figure 4.1 means, because you will
be seeing this a lot.
Anil’s choices are the rows of the table and Bala’s are the columns. We
call Anil the ‘row player’ and Bala the ‘column player’.
When an interaction is represented in a table like Figure 4.1, each entry
describes the outcome of a hypothetical situation. For example, the upper-
left cell should be interpreted as:
Suppose (for whatever reason) Anil planted rice and Bala planted rice
too. What would we see?
There are four possible hypothetical situations. Figure 4.1 describes what
would happen in each case.
To simplify the model, we assume that:
• There are no other people involved or affected in any way.
• The selection of which crop to grow is the only decision that Anil and
Bala need to make.
Both produce rice: there
is a glut of rice (low price)
There is a shortage
of cassava
Anil not producing cassava,
which he is better able
to produce
No market glut
High prices for both crops
Both farmers producing the
crop for which they are
less suited
No market glut
High prices for both crops
Both farmers producing the
crop for which they are
better suited
Both produce cassava:
there is a glut of cassava
(low price)
There is a shortage of rice
Bala not producing rice,
which he is better able
to produce
Rice Cassava
Bala
Ca
ss
av
a
Ri
ce
An
il
Figure 4.1 Social interactions in the invisible hand game.
4.1 SOCIAL INTERACTIONS: GAME THEORY
135
payoff The benefit to each player
associated with the joint actions of
all the players.
• Anil and Bala will interact just once (this is called a ‘one-shot game’).
• They decide simultaneously. When a player makes a decision, that player
doesn’t know what the other person has decided to do.
Figure 4.2a shows the payoffs for Anil and Bala in each of the four
hypothetical situations—the incomes they would receive if the hypothetical
row and column actions were taken. Since their incomes depend on the
market prices, which in turn depend on their decisions, we have called this
an ‘invisible hand’ game.
• Because the market price falls when it is flooded with one crop, they can
do better if they specialize compared to when they both produce the
same good.
• When they produce different goods they would both do better if each
person specialized in the crop that was most suitable for their land.
Anil gets 1
Bala gets 3
Both get 2
Both get 4 Anil gets 3
Bala gets 1
Rice Cassava
Bala
Ca
ss
av
a
Ri
ce
An
il
Figure 4.2a The payoffs in the invisible hand game.
UNIT 4 SOCIAL INTERACTIONS
136
best response In game theory, the
strategy that will give a player the
highest payoff, given the strategies
that the other players select.
dominant strategy Action that
yields the highest payoff for a
player, no matter what the other
players do.
dominant strategy equilibrium An
outcome of a game in which every
player plays his or her dominant
strategy.
QUESTION 4.1 CHOOSE THE CORRECT ANSWER(S)
In a simultaneous one-shot game:
A player observes what others do before deciding how to act.
A player decides his or her action, taking into account what other
players may do after knowing his or her move.
Players coordinate to find the actions that lead to the optimal out-
come for society.
A player chooses an action taking into account the possible actions
that other players can take.
4.2 EQUILIBRIUM IN THE INVISIBLE HAND GAME
Game theory describes social interactions, but it may also provide
predictions about what will happen. To predict the outcome of a game, we
need another concept: best response. This is the strategy that will give a
player the highest payoff, given the strategies the other players select.
In Figure 4.2b we represent the payoffs for Anil and Bala in the invisible
hand game using a standard format called a payoff matrix. A matrix is just
any rectangular (in this case square) array of numbers. The first number in
each box is the reward received by the row player (whose name begins with
A as a reminder that his payoff is first). The second number is the column
player’s payoff.
Think about best responses in this game. Suppose you are Anil, and you
consider the hypothetical case in which Bala has chosen to grow rice.
Which response yields you the higher payoff? You would grow cassava (in
this case, you—Anil—would get a payoff of 4, but you would get a payoff of
only 1 if you grew rice instead).
Work through the steps in Figure 4.2b to see that choosing Cassava is
also Anil’s best response if Bala chooses Cassava. So Cassava is Anil’s
dominant strategy: it will give him the highest payoff, whatever Bala does.
And you will see that in this game Bala also has a dominant strategy. The
analysis also gives you a handy method for keeping track of best responses
by placing dots and circles in the payoff matrix.
Because both players have a dominant strategy, we have a simple
prediction about what each will do: play their dominant strategy. Anil will
grow cassava, and Bala will grow rice.
This pair of strategies is a dominant strategy equilibrium of the game.
Remember from Unit 2 that an equilibrium is a self-perpetuating situ-
ation. Something of interest does not change. In this case, Anil choosing
Cassava and Bala choosing Rice is an equilibrium because neither of them
would want to change their decision after seeing what the other player
chose.
If we find that both players in a two-player game have dominant
strategies, the game has a dominant strategy equilibrium. As we will see
later, this does not always happen. But when it does, we predict that these
are the strategies that will be played.
Because both Anil and Bala have a dominant strategy, their choice of
crop is not affected by what they expect the other person to do. This is
similar to the models in Unit 3 in which Alexei’s choice of hours of study, or
Angela’s working hours, did not depend on what others did. But here, even
though the decision does not depend on what the others do, the payoff
4.2 EQUILIBRIUM IN THE INVISIBLE HAND GAME
137
does. For example, if Anil is playing his dominant strategy (Cassava) he is
better off if Bala plays Rice than if Bala plays Cassava as well.
In the dominant strategy equilibrium Anil and Bala have specialized in
producing the good for which their land is better suited. Simply pursuing
their self-interest—choosing the strategy for which they got the highest
payoff—resulted in an outcome that was:
• the best of the four possible outcomes for each player
• the strategy that yielded the largest total payoffs for the two farmers
combined
In this example, the dominant strategy equilibrium is the outcome that each
would have chosen if they had a way of coordinating their decisions.
Although they independently pursued their self-interest, they were guided
Rice Cassava
Bala
3
1
2
2
4
4
1
3Ca
ss
av
a
Ri
ce
An
il
Figure 4.2b The payoff matrix in the invisible hand game.
1. Finding best responses
Begin with the row player (Anil) and
ask: ‘What would be his best response
to the column player’s (Bala’s) decision
to play Rice?’
2. Anil’s best response if Bala grows rice
If Bala chooses Rice, Anil’s best
response is to choose Cassava—that
gives him 4, rather than 1. Place a dot
in the bottom left-hand cell. A dot in a
cell means that this is the row player’s
best response.
3. Anil’s best response if Bala grows
cassava
If Bala chooses Cassava, Anil’s best
response is to choose Cassava too—
giving him 3, rather than 2. Place a dot
in the bottom right-hand cell.
4. Anil has a dominant strategy
Both dots are on the bottom row.
Whatever Bala’s choice, Anil’s best
response is to choose Cassava. Cassava
is a dominant strategy for Anil.
5. Now find the column player’s best
responses
If Anil chooses Rice, Bala’s best
response is to choose Rice (3 rather
than 2). Circles represent the column
player’s best responses. Place a circle
in the upper left-hand cell.
6. Bala has a dominant strategy too
If Anil chooses Cassava, Bala’s best
response is again to choose Rice (he
gets 4 rather than 1). Place a circle in
the lower left-hand cell. Rice is Bala’s
dominant strategy (both circles are in
the same column).
7. Both players will play their dominant
strategies
We predict that Anil will choose
Cassava and Bala will choose Rice
because that is their dominant strategy.
Where the dot and circle coincide, the
players are both playing best responses
to each other.
UNIT 4 SOCIAL INTERACTIONS
138
‘as if by an invisible hand’ to an outcome that was in both of their best
interests.
Real economic problems are never this simple, but the basic logic is the
same. The pursuit of self-interest without regard for others is sometimes
considered to be morally bad, but the study of economics has identified
cases in which it can lead to outcomes that are socially desirable. There are
other cases, however, in which the pursuit of self-interest leads to results
that are not in the self-interest of any of the players. The prisoners’
dilemma game, which we study next, describes one of these situations.
QUESTION 4.2 CHOOSE THE CORRECT ANSWER(S)
Brian likes going to the cinema more than watching football. Anna, on
the other hand, prefers watching football to going to the cinema. If one
person chooses his or her favourite activity, the other person prefers to
spend time together rather than spend an afternoon apart. The follow-
ing table represents the happiness levels (payoffs) of Anna and Brian,
depending on their choice of activity (the first number is Brian’s
happiness level while the second number is Anna’s):
Football Cinema
Anna
5
3
1
1
3
4
2
6
Br
ia
n
Ci
ne
m
a
Fo
ot
ba
ll
Based on the information above, we can conclude that:
The dominant strategy for both players is Football.
There is no dominant strategy equilibrium.
The dominant strategy equilibrium yields the highest possible
happiness for both.
Neither player would want to deviate from the dominant strategy
equilibrium.
4.2 EQUILIBRIUM IN THE INVISIBLE HAND GAME
139
Francis Ysidro Edgeworth. 2003.
Mathematical Psychics and Further
Papers on Political Economy.
Oxford: Oxford University Press.
H. L. Mencken. 2006. A Little Book
in C Major. New York, NY: Kessinger
Publishing.
reciprocity A preference to be kind
or to help others who are kind and
helpful, and to withhold help and
kindness from people who are not
helpful or kind.
inequality aversion A dislike of out-
comes in which some individuals
receive more than others.
WHEN ECONOMISTS DISAGREE
Homo economicus in question: Are people entirely selfish?
For centuries, economists and just about everyone else have debated
whether people are entirely self-interested or are sometimes happy to
help others even when it costs them something to do so. Homo eco-
nomicus (economic man) is the nickname given to the selfish and
calculating character that you find in economics textbooks. Have eco-
nomists been right to imagine homo economicus as the only actor on the
economic stage?
In the same book in which he first used the phrase ‘invisible hand’,
Adam Smith also made it clear that he thought we were not homo eco-
nomicus: ‘How selfish soever man may be supposed, there are evidently
some principles in his nature which interest him in the fortunes of
others, and render their happiness necessary to him, though he derives
nothing from it except the pleasure of seeing it.’ (The Theory of Moral
Sentiments, 1759)
But most economists since Smith have disagreed. In 1881, Francis
Edgeworth, a founder of modern economics, made this perfectly clear in
his book Mathematical Psychics: ‘The first principle of economics is that
every agent is actuated only by self-interest.’
Yet everyone has experienced, and sometimes even performed, great
acts of kindness or bravery on behalf of others in situations in which
there was little chance of a reward. The question for economists is:
should the unselfishness evident in these acts be part of how we reason
about behaviour?
Some say ‘no’: many seemingly generous acts are better understood
as attempts to gain a favourable reputation among others that will bene-
fit the actor in the future.
Maybe helping others and observing social norms is just self-interest
with a long time horizon. This is what the essayist H. L. Mencken
thought: ‘conscience is the inner voice which warns that somebody may
be looking.’
Since the 1990s, in an attempt to resolve the debate on empirical
grounds, economists have performed hundreds of experiments all over
the world in which the behaviour of individuals (students, farmers,
whale hunters, warehouse workers, and CEOs) can be observed as they
make real choices about sharing, using economic games.
In these experiments, we almost always see some self-interested
behaviour. But we also observe altruism, reciprocity, aversion to
inequality, and other preferences that are different from self-interest.
In many experiments homo economicus is the minority. This is true even
when the amounts being shared (or kept for oneself) amount to many
days’ wages.
Is the debate resolved? Many economists think so and now consider
people who are sometimes altruistic, sometimes inequality averse, and
sometimes reciprocal, in addition to homo economicus. They point out
that the assumption of self-interest is appropriate for many economic
settings, like shopping or the way that firms use technology to maximize
profits. But it’s not as appropriate in other settings, such as how we pay
taxes, or why we work hard for our employer.
UNIT 4 SOCIAL INTERACTIONS
140
•4.3 THE PRISONERS’ DILEMMA
Imagine that Anil and Bala are now facing a different problem. Each is
deciding how to deal with pest insects that destroy the crops they cultivate
in their adjacent fields. Each has two feasible strategies:
• The first is to use an inexpensive chemical called Terminator. It kills
every insect for miles around. Terminator also leaks into the water
supply that they both use.
• The second is to use integrated pest control (IPC) instead of a chemical.
A farmer using IPC introduces beneficial insects to the farm. The
beneficial insects eat the pest insects.
If just one of them chooses Terminator, the damage is quite limited. If they
both choose it, water contamination becomes a serious problem, and they
need to buy a costly filtering system. Figures 4.3a and 4.3b describe their
interaction.
Both Anil and Bala are aware of these outcomes. As a result, they know
that their payoff (the amount of money they will make at harvest time,
minus the costs of their pest control strategy and the installation of water
filtration if that becomes necessary), will depend not only on what choice
they make, but also on the other’s choice. This is a strategic interaction.
How will they play the game? To figure this out, we can use the same
method as in the previous section (draw the dots and circles in the payoff
matrix for yourself).
Beneficial insects spread
over both fields,
eliminating pests
No water contamination
Bala’s chemicals spread to
Anil’s field and kill his
beneficial insects
Limited water contamination
Anil’s chemicals spread to
Bala’s field and kill his
beneficial insects
Limited water contamination
Eliminates all pests
Heavy water contamination
Requires costly
filtration system
IPC Terminator
Bala
Te
rm
in
at
or
IP
C
An
il
Figure 4.3a Social interactions in the pest control game.
4.3 THE PRISONERS’ DILEMMA
141
prisoners’ dilemma A game in
which the payoffs in the dominant
strategy equilibrium are lower for
each player, and also lower in total,
than if neither player played the
dominant strategy.
Anil’s best responses:
• If Bala chooses IPC: Terminator (cheap eradication of pests, with little
water contamination).
• If Bala chooses Terminator: Terminator (IPC costs more and cannot work
since Bala’s chemicals will kill beneficial pests).
So Terminator is Anil’s dominant strategy.
You can check, similarly, that Terminator is also a dominant strategy for
Bala.
Because Terminator is the dominant strategy for both, we predict that
both will use it. Both players using insecticide is the dominant strategy
equilibrium of the game.
Anil and Bala each receive payoffs of 2. But both would be better off if
they both used IPC instead. So the predicted outcome is not the best feas-
ible outcome. The pest control game is a particular example of a game
called the prisoners’ dilemma.
The contrast between the invisible hand game and the prisoners’
dilemma shows that self-interest can lead to favourable outcomes, but can
also lead to outcomes that nobody would endorse. Such examples can help
us understand more precisely how markets can harness self-interest to
improve the workings of the economy, but also the limitations of markets.
Three aspects of the interaction between Anil and Bala caused us to
predict an unfortunate outcome in their prisoners’ dilemma game:
• They did not place any value on the payoffs of the other person, and so
did not internalize (take account of) the costs that their actions inflicted
on the other.
• There was no way that Anil, Bala or anyone else could make the farmer
who used the insecticide pay for the harm that it caused.
• They were not able to make an agreement beforehand about what each
would do. Had they been able to do so, they could have simply agreed to
use IPC, or banned the use of Terminator.
IPC Terminator
Bala
3
3
4
1
1
4
2
2
An
il
IP
C
Te
rm
in
at
or
Figure 4.3b Payoff matrix for the pest control game.
UNIT 4 SOCIAL INTERACTIONS
142
A solution to the prisoners’
dilemma on the show Golden Balls
https://tinyco.re/5782321
The prisoners’ dilemma
The name of this game comes from a story about two prisoners (we call
them Thelma and Louise) whose strategies are either to Accuse
(implicate) the other in a crime that the prisoners may have committed
together, or Deny that the other prisoner was involved.
If both Thelma and Louise deny it, they are freed after a few days of
questioning.
If one person accusing the other person, while the other person
denies, the accuser will be freed immediately (a sentence of zero years),
whereas the other person gets a long jail sentence (10 years).
Lastly, if both Thelma and Louise choose Accuse (meaning each
implicates the other), they both get a jail sentence. This sentence is
reduced from 10 years to 5 years because of their cooperation with the
police. The payoffs of the game are shown in Figure 4.4.
Deny Accuse
Louise
1
1
0
10
10
0
5
5
Th
el
m
a
D
en
y
Ac
cu
se
Figure 4.4 Prisoners’ dilemma (payoffs are years in prison).
(The payoffs are written in terms of years of prison—so Louise and
Thelma prefer lower numbers.)
In a prisoners’ dilemma, both players have a dominant strategy (in
this example, Accuse) which, when played by both, results in an out-
come that is worse for both than if they had both adopted a different
strategy (in this example, Deny).
Our story about Thelma and Louise is hypothetical, but this game
applies to many real problems. For example, watch the clip from a TV
quiz show called Golden Balls (https://tinyco.re/5782321), and you will
see how one ordinary person ingeniously resolves the prisoners’
dilemma.
In economic examples, the mutually beneficial strategy (Deny) is
generally termed Cooperate, while the dominant strategy (Accuse) is
called Defect. Cooperate does not mean that players get together and
discuss what to do. The rules of the game are always that each player
decides independently on a strategy.
If we can overcome one or more of these problems, the outcome preferred
by both of them would sometimes result. So, in the rest of this unit, we will
examine ways to do this.
4.3 THE PRISONERS’ DILEMMA
143
QUESTION 4.3 CHOOSE THE CORRECT ANSWER(S)
Dimitrios and Ameera work for an international investment bank as
foreign exchange traders. They are being questioned by the police on
their suspected involvement in a series of market manipulation trades.
The table below shows the cost of each strategy (in terms of the length
in years of jail sentences they will receive), depending on whether they
accuse each other or deny the crime. The first number is the payoff to
Dimitrios, while the second number is the payoff to Ameera (the neg-
ative numbers signify losses). Assume that the game is a simultaneous
one-shot game.
Deny Accuse
Ameera
–2
–2
0
–15
–15
0
–8
–8
D
im
itr
io
s
Ac
cu
se
D
en
y
Based on this information, we can conclude that:
Both traders will hold out and deny their involvement.
Both traders will accuse each other, even though they will end up
being in jail for eight years.
Ameera will accuse, whatever she expects Dimitrios to do.
There is a small possibility that both traders will get away with two
years each.
EXERCISE 4.2 POLITICAL ADVERTISING
Many people consider political advertising (campaign advertisements) to
be a classic example of a prisoners’ dilemma.
1. Using examples from a recent political campaign with which you are
familiar, explain whether this is the case.
2. Write down an example payoff matrix for this case.
•4.4 SOCIAL PREFERENCES: ALTRUISM
When students play one-shot prisoners’ dilemma games in classroom or
laboratory experiments—sometimes for substantial sums of real money—it
is common to observe half or more of the participants playing the
Cooperate rather than Defect strategy, despite mutual defection being the
dominant strategy for players who care only about their own monetary
payoffs. One interpretation of these results is that players are altruistic.
UNIT 4 SOCIAL INTERACTIONS
144
social preferences Preferences
that place a value on what happens
to other people, even if it results in
lower payoffs for the individual.
zero sum game A game in which
the payoff gains and losses of the
individuals sum to zero, for all com-
binations of strategies they might
pursue.
For example, if Anil had cared sufficiently about the harm that he would
inflict on Bala by using Terminator when Bala was using IPC, then IPC
would have been Anil’s best response to Bala’s IPC. And if Bala had felt the
same way, then IPC would have been a mutual best response, and the two
would no longer have been in a prisoners’ dilemma.
A person who is willing to bear a cost in order to help another person is
said to have altruistic preferences. In the example just given, Anil was
willing to give up 1 payoff unit because that would have imposed a loss of 2
on Bala. The cost to him of choosing IPC when Bala had chosen IPC was 1,
and it conferred a benefit of 2 on Bala, meaning that he had acted
altruistically.
The economic models we used in Unit 3 assumed self-interested prefer-
ences: Alexei, the student, and Angela, the farmer, cared about their own
free time and their own grades or consumption. People generally do not
care only about what happens to themselves, but also what happens to
others. Then we say that the individual has social preferences. Altruism is
an example of a social preference. Spite and envy are also social prefer-
ences.
Altruistic preferences as indifference curves
In previous units, we used indifference curves and feasible sets to model
Alexei’s and Angela’s behaviour. We can do the same to study how people
interact when social preferences are part of their motivation.
Imagine the following situation. Anil was given some tickets for the
national lottery, and one of them won a prize of 10,000 rupees. He can, of
course, keep all the money for himself, but he can also share some of it with
his neighbour Bala. Figure 4.5 represents the situation graphically. The
horizontal axis represents the amount of money (in thousands of rupees)
that Anil keeps for himself, and the vertical one the amount that he gives to
Bala. Each point (x, y) represents a combination of amounts of money for
Anil (x) and Bala (y) in thousands of rupees. The shaded triangle depicts the
feasible choices for Anil. At the corner (10, 0) on the horizontal axis, Anil
keeps it all. At the other corner (0, 10) on the vertical axis, Anil gives it all to
Bala. Anil’s feasible set is the shaded area.
The boundary of the shaded area is the feasible frontier. If Anil is
dividing up his prize money between himself and Bala, he chooses a point
on that frontier (being inside the frontier would mean throwing away some
of the money). The choice among points on the feasible frontier is called a
zero sum game because, when choosing point B rather than point A as in
Figure 4.5, the sum of Anil’s losses and Bala’s gains is zero (for example,
Anil has 3,000 fewer rupees at B than at A, and Bala has 3,000 rupees at B
and nothing at A).
Anil’s preferences can be represented by indifference curves, showing
combinations of the amounts for Anil and Bala that are all equally preferred
by Anil. Figure 4.5 illustrates two cases. In the first, Anil has self-interested
preferences so his indifference curves are straight vertical lines; in the
second he is somewhat altruistic—he cares about Bala—so his indifference
curves are downward-sloping.
If Anil is self-interested, the best option given his feasible set is A, where
he keeps all the money. If he derives utility from Bala’s consumption, he has
downward-sloping indifference curves so he may prefer an outcome where
Bala gets some of the money.
4.4 SOCIAL PREFERENCES: ALTRUISM
145
With the specific indifference curves shown in Figure 4.5, the best feas-
ible option for Anil is point B (7, 3) where Anil keeps 7,000 rupees and gives
3,000 to Bala. Anil prefers to give 3,000 rupees to Bala, even at a cost of
3,000 rupees to him. This is an example of altruism: Anil is willing to bear a
cost to benefit somebody else.
EXERCISE 4.3 ALTRUISM AND SELFLESSNESS
Using the same axes as in Figure 4.5:
1. What would Anil’s indifference curves look like if he cared just as much
about Bala’s consumption as his own?
2. What would they look like if he derived utility only from the total of his
and Bala’s consumption?
3. What would they look like if he derived utility only from Bala’s con-
sumption?
4. For each of these cases, provide a real world situation in which Anil
might have these preferences, making sure to specify how Anil and
Bala derive their payoffs.
Leibniz: Finding the optimal distri-
bution with altruistic preferences
(https://tinyco.re/L040401)
Ba
la
’s
pa
yo
ff
(t
ho
us
an
ds
o
f r
up
ee
s)
Anil’s payoff (thousands of rupees)
12
10
5
3
0
0 6 7 10 12
Feasible
payoffs set
Feasible
payoffs
frontier
Anil’s indifference curves
(when somewhat altruistic)
Anil’s indifference
curves (when completely selfish)
A
B
C
Figure 4.5 How Anil chooses to distribute his lottery winnings depends on whether
he is selfish or altruistic.
1. Feasible payoffs
Each point (x, y) in the figure represents
a combination of amounts of money for
Anil (x) and Bala (y), in thousands of
rupees. The shaded triangle depicts the
feasible choices for Anil.
2. Indifference curves when Anil is
self-interested
If Anil does not care at all about what
Bala gets, his indifference curves are
straight vertical lines. He is indifferent
to whether Bala gets a lot or nothing.
He prefers curves further to the right,
since he gets more money.
3. Anil’s best option
Given his feasible set, Anil’s best option
is A, where he keeps all the money.
4. What if Anil cares about Bala?
But Anil may care about his neighbour
Bala, in which case he is happier if Bala
is richer: that is, he derives utility from
Bala’s consumption. In this case he has
downward-sloping indifference curves.
5. Anil’s indifference curves when he is
somewhat altruistic
Points B and C are equally preferred by
Anil, so Anil keeping 7 and Bala getting
3 is just as good in Anil’s eyes as Anil
getting 6 and Bala getting 5. His best
feasible option is point B.
UNIT 4 SOCIAL INTERACTIONS
146
QUESTION 4.4 CHOOSE THE CORRECT ANSWER(S)
In Figure 4.5 (page 146) Anil has just won the lottery and has received
10,000 rupees. He is considering how much (if at all) he would like to
share this sum with his friend Bala. Before he manages to share his
winnings, Anil receives a tax bill for these winnings of 3,000 rupees.
Based on this information, which of the following statements is true?
Bala will receive 3,000 rupees if Anil is somewhat altruistic.
If Anil was somewhat altruistic and kept 7,000 rupees before the tax
bill, he will still keep 7,000 rupees after the tax bill by turning
completely selfish.
Anil will be on a lower indifference curve after the tax bill.
Had Anil been so extremely altruistic that he only cared about
Bala’s share, then Bala would have received the same income
before and after the tax bill.
•4.5 ALTRUISTIC PREFERENCES IN THE PRISONERS’
DILEMMA
When Anil and Bala wanted to get rid of pests (Section 4.3), they found
themselves in a prisoners’ dilemma. One reason for the unfortunate out-
come was that they did not account for the costs that their actions inflicted
on the other. The choice of pest control regime using the insecticide
implied a free ride on the other farmer’s contribution to ensuring clean
water.
If Anil cares about Bala’s wellbeing as well as his own, the outcome can
be different.
In Figure 4.6 (page 148) the two axes now represent Anil and Bala’s
payoffs. Just as with the example of the lottery, the diagram shows the feas-
ible outcomes. However, in this case the feasible set has only four points.
We have shortened the names of the strategies for convenience: Terminator
is T, IPC is I. Notice that movements upward and to the right from (T, T) to
(I, I) are win-win: both get higher payoffs. On the other hand, moving up,
and to the left, or down, and to the right—from (I, T) to (T, I) or the
reverse—are win-lose changes. Win-lose means that Bala gets a higher
payoff at the expense of Anil, or Anil benefits at the expense of Bala.
As in the case of dividing lottery winnings, we look at two cases. If Anil
does not care about Bala’s wellbeing, his indifference curves are vertical
lines. If he does care, he has downward-sloping indifference curves. Work
through Figure 4.6 to see what will happen in each case.
Figure 4.6 demonstrates that when Anil is completely self-interested, his
dominant strategy is Terminator (as we saw before). But if Anil cares
sufficiently about Bala, his dominant strategy is IPC. If Bala feels the same
way, then the two would both choose IPC, resulting in the outcome that
both of them prefer the most.
The main lesson is that if people care about one another, social
dilemmas are easier to resolve. This helps us understand the historical
examples in which people mutually cooperate for irrigation or enforce the
Montreal Protocol to protect the ozone layer, rather than free riding on the
cooperation of others.
4.5 ALTRUISTIC PREFERENCES IN THE PRISONERS’ DILEMMA
147
QUESTION 4.5 CHOOSE THE CORRECT ANSWER(S)
Figure 4.6 shows Anil’s preferences when he is completely selfish, and
also when he is somewhat altruistic, when he and Bala participate in
the prisoners’ dilemma game.
Based on the graph, we can say that:
When Anil is completely selfish, using Terminator is his dominant
strategy.
When Anil is somewhat altruistic, using Terminator is his dominant
strategy.
When Anil is completely selfish, (T, T) is the dominant strategy equi-
librium even though it is on a lower indifference curve for him than
(T, I).
If Anil is somewhat altruistic, and Bala’s preferences are the same
as Anil’s, (I, I) is attained as the dominant strategy equilibrium.
Ba
la
’s
pa
yo
ff
Anil’s payoff
5
4
0
1
2
3
0 54321
Anil’s indifference
curves
(when somewhat
altruistic)
Anil’s indifference
curves (when
completely
selfish)
I, T
I, I
T, T
T, I
IPC Terminator
Bala
3
3
4
1
1
4
2
2
An
il
IP
C
Te
rm
in
at
or
Figure 4.6 Anil’s decision to use IPC (I) or Terminator (T) as his crop management
strategy depends on whether he is completely selfish or somewhat altruistic.
1. Anil and Bala’s payoffs
The two axes in the figure represent
Anil and Bala’s payoffs. The four points
are the feasible outcomes associated
to the strategies.
2. Anil’s indifference curves if he
doesn’t care about Bala
If Anil does not care about Bala’s
wellbeing, his indifference curves are
vertical, so (T, I) is his most preferred
outcome. He prefers (T, I) to (I, I), so
should choose T if Bala chooses I. If
Anil is completely selfish, T is
unambiguously his best choice.
3. Anil’s indifference curves when he
cares about Bala
When Anil cares about Bala’s
wellbeing, indifference curves are
downward-sloping and (I, I) is his most
preferred outcome. If Bala chooses I,
Anil should choose I. Anil should also
choose I if Bala chooses T, since he
prefers (I, T) to (T, T).
UNIT 4 SOCIAL INTERACTIONS
148
public good A good for which use
by one person does not reduce its
availability to others. Also known
as: non-rival good. See also: non-
excludable public good, artificially
scarce good.
EXERCISE 4.4 AMORAL SELF-INTEREST
Imagine a society in which everyone was entirely self-interested (cared
only about his or her own wealth) and amoral (followed no ethical rules
that would interfere with gaining that wealth). How would that society be
different from the society you live in? Consider the following:
• families
• workplaces
• neighbourhoods
• traffic
• political activity (would people vote?)
•4.6 PUBLIC GOODS, FREE RIDING, AND REPEATED
INTERACTION
Now let’s look at the second reason for an unfortunate outcome in the
prisoners’ dilemma game. There was no way that either Anil or Bala (or
anyone else) could make whoever used the insecticide pay for the harm that
it caused.
The problems of Anil and Bala are hypothetical, but they capture the real
dilemmas of free riding that many people around the world face. For
example, as in Spain, many farmers in southeast Asia rely on a shared
irrigation facility to produce their crops. The system requires constant
maintenance and new investment. Each farmer faces the decision of how
much to contribute to these activities. These activities benefit the entire
community and if the farmer does not volunteer to contribute, others may
do the work anyway.
Imagine there are four farmers who are deciding whether to contribute
to the maintenance of an irrigation project.
For each farmer, the cost of contributing to the project is $10. But when
one farmer contributes, all four of them will benefit from an increase in
their crop yields made possible by irrigation, so they will each gain $8.
Contributing to the irrigation project is called a public good: when one
individual bears a cost to provide the good, everyone receives a benefit.
Now, consider the decision facing Kim, one of the four farmers. Figure
4.7 shows how her decision depends on her total earnings, but also on the
number of other farmers who decide to contribute to the irrigation project.
For example, if two of the others contribute, Kim will receive a benefit
of $8 from each of their contributions. So if she makes no contribution
herself, her total payoff, shown in red, is $16. If she decides to contribute,
she will receive an additional benefit of $8 (and so will the other three
farmers). But she will incur a cost of $10, so her total payoff is $14, as in
Figure 4.7, and as calculated in Figure 4.8.
Figures 4.7 and 4.8 illustrate the social dilemma. Whatever the other
farmers decide to do, Kim makes more money if she doesn’t contribute than
if she does. Not contributing is a dominant strategy. She can free ride on
the contributions of the others.
This public goods game is a prisoners’ dilemma in which there are more
than two players. If the farmers care only about their own monetary payoff,
there is a dominant strategy equilibrium in which no one contributes and
their payoffs are all zero. On the other hand, if all contributed, each would
4.6 PUBLIC GOODS, FREE RIDING, AND REPEATED INTERACTION
149
get $22. Everyone would benefit if everyone cooperated, but irrespective of
what others do, each farmer does better by free riding on the others.
Altruism could help to solve the free rider problem: if Kim cared about
the other farmers, she might be willing to contribute to the irrigation
project. But if large numbers of people are involved in a public goods game,
it is less likely that altruism will be sufficient to sustain a mutually
beneficial outcome.
Yet around the world, real farmers and fishing people have faced public
goods situations in many cases with great success. The evidence gathered
by Elinor Ostrom, a political scientist, and other researchers on common
irrigation projects in India, Nepal, and other countries, shows that the
degree of cooperation varies. In some communities a history of trust
encourages cooperation. In others, cooperation does not happen. In south
India, for example, villages with extreme inequalities in land and caste
status had more conflicts over water usage. Less unequal villages
maintained irrigation systems better: it was easier to sustain cooperation.
Elinor Ostrom. 2000. ‘Collective
Action and the Evolution of Social
Norms’. Journal of Economic
Perspectives 14 (3): pp. 137–58.
Ki
m
's
pa
yo
ff
($
)
–8
0
8
15
23
30
Number of other farmers contributing
0 1 2 3
Kim's payoff if she contributes
Kim's payoff if she does not contribute
−2
24
16
8
0
22
14
6
Figure 4.7 Kim’s payoffs in the public goods game.
Benefit from the contribution of others 16
Plus benefit from her own contribution + 8
Minus cost of her contribution – 10
Total $14
Figure 4.8 Example: When two others contribute, Kim’s payoff is lower if she
contributes too.
UNIT 4 SOCIAL INTERACTIONS
150
social norm An understanding that
is common to most members of a
society about what people should
do in a given situation when their
actions affect others.
GREAT ECONOMISTS
Elinor Ostrom
The choice of Elinor Ostrom
(1933–2012), a political scientist,
as a co-recipient of the 2009 Nobel
Prize surprised most economists.
For example, Steven Levitt, a
professor at the University of
Chicago, admitted he knew
nothing about her work, and had
‘no recollection of ever seeing or
hearing her name mentioned by an
economist’.
Some, however, vigorously
defended the decision. Vernon
Smith, an experimental economist who had previously been awarded the
Prize, congratulated the Nobel committee for recognizing her
originality, ‘scientific common sense’ and willingness to listen ‘carefully
to data’.
Ostrom’s entire academic career was focused on a concept that plays
a central role in economics but is seldom examined in much detail:
property. Ronald Coase had established the importance of clearly
delineated property rights when one person’s actions affected the
welfare of others. But Coase’s main concern was the boundary between
the individual and the state in regulating such actions. Ostrom explored
the middle ground where communities, rather than individuals or
formal governments, held property rights.
The conventional wisdom at the time was that informal collective
ownership of resources would lead to a ‘tragedy of the commons’. That
is, economists believed that resources could not be used efficiently and
sustainably under a common property regime. Thanks to Elinor Ostrom
this is no longer a dominant view.
First, she made a distinction between resources held as common
property and those subject to open access:
• Common property involves a well-defined community of users who
are able in practice, if not under the law, to prevent outsiders from
exploiting the resource. Inshore fisheries, grazing lands, or forest
areas are examples.
• Open-access resources such as ocean fisheries or the atmosphere as a
carbon sink, can be exploited without restrictions, other than those
imposed by states acting alone or through international agreements.
Ostrom was not alone in stressing this distinction, but she drew on a
unique combination of case studies, statistical methods, game theoretic
models with unorthodox ingredients, and laboratory experiments to try
to understand how tragedies of the commons could be averted.
She discovered great diversity in how common property is managed.
Some communities were able to devise rules and draw on social norms
to enforce sustainable resource use, while others failed to do so. Much of
her career was devoted to identifying the criteria for success, and using
4.6 PUBLIC GOODS, FREE RIDING, AND REPEATED INTERACTION
151
Elinor Ostrom, James Walker, and
Roy Gardner. 1992. ‘Covenants
With and Without a Sword: Self-
Governance is Possible’. The
American Political Science Review
86 (2).
Anil:
Social preferences partly explain why these communities avoid Garrett
Hardin’s tragedy of the commons. But they may also find ways of deterring
free-riding behaviour.
Repeated games
Free riding today on the contributions of other members of one’s
community may have unpleasant consequences tomorrow or years from
now. Ongoing relationships are an important feature of social interactions
that was not captured in the models we have used so far: life is not a one-
shot game.
The interaction between Anil and Bala in our model was a one-shot
game. But as owners of neighbouring fields, Anil and Bala are more
realistically portrayed as interacting repeatedly.
Imagine how differently things would work out if we represented their
interaction as a game to be repeated each season. Suppose that Bala has
adopted IPC. What is Anil’s best response? He would reason like this:
If I play IPC, then maybe Bala will continue to do so, but if I use
Terminator—which would raise my profits this season—Bala would
theory to understand why some arrangements worked well while others
did not.
Many economists believed that the diversity of outcomes could be
understood using the theory of repeated games, which predicts that even
when all individuals care only for themselves, if interactions are
repeated with sufficiently high likelihood and individuals are patient
enough, then cooperative outcomes can be sustained indefinitely.
But this was not a satisfying explanation for Ostrom, partly because
the same theory predicted that any outcome, including rapid depletion,
could also arise.
More importantly, Ostrom knew that sustainable use was enforced
by actions that clearly deviated from the hypothesis of material self-
interest. In particular, individuals would willingly bear considerable
costs to punish violators of rules or norms. As the economist Paul
Romer put it, she recognized the need to ‘expand models of human pref-
erences to include a contingent taste for punishing others’.
Ostrom developed simple game theoretic models in which indi-
viduals have unorthodox preferences, caring directly about trust and
reciprocity. And she looked for the ways in which people faced with a
social dilemma avoided tragedy by changing the rules so that the
strategic nature of the interaction was transformed.
She worked with economists to run a pioneering series of
experiments, confirming the widespread use of costly punishment in
response to excessive resource extraction, and also demonstrated the
power of communication and the critical role of informal agreements in
supporting cooperation. Thomas Hobbes, a seventeenth-century
philosopher, had asserted that agreements had to be enforced by govern-
ments, since ‘covenants, without the sword, are but words and of no
strength to secure a man at all’. Ostrom disagreed. As she wrote in the
title of an influential article, covenants—even without a sword—make
self-governance possible.
UNIT 4 SOCIAL INTERACTIONS
152
The Experiencing Economics ebook
(https://www.core-econ.org/
experiencing-economics) contains
a public goods game that you can
play with your students in the
classroom or during synchronous
online teaching. Visit the
instructor’s section to find a step-
by-step guide for running the game.
use Terminator next year. So unless I am extremely impatient for
income now, I’d better stick with IPC.
Bala could reason in exactly the same way. The result might be that they
would then continue playing IPC forever.
In the next section, we will look at experimental evidence of how people
behave when a public goods game is repeated.
QUESTION 4.6 CHOOSE THE CORRECT ANSWER(S)
Four farmers are deciding whether to contribute to the maintenance of
an irrigation project. For each farmer, the cost of contributing to the
project is $10. But for each farmer who contributes, all four of them
will benefit from an increase in their crop yields, so they will each gain
$8 per farmer that contributes.
Which of the following statements is correct?
If all the farmers are selfish, none of them will contribute.
If one of the farmers, Kim, cares about her neighbour Jim just as
much as herself, she will contribute $10.
If Kim is altruistic and contributes $10, the others might contribute
too, even if they are selfish.
If the farmers have to reconsider this decision every year, they
might choose to contribute to the project even if they are selfish.
4.7 PUBLIC GOOD CONTRIBUTIONS AND PEER
PUNISHMENT
An experiment demonstrates that people can sustain high levels of cooperation
in a public goods game, as long as they have opportunities to target free riders
once it becomes clear who is contributing less than the norm.
Figure 4.9a shows the results of laboratory experiments that mimic the
costs and benefits from contribution to a public good in the real world. The
experiments were conducted in cities around the world. In each experiment
participants play 10 rounds of a public goods game, similar to the one
involving Kim and the other farmers that we just described. In each round, the
people in the experiment (we call them subjects) are given $20. They are
randomly sorted into small groups, typically of four people, who don’t know
each other. They are asked to decide on a contribution from their $20 to a
common pool of money. The pool is a public good. For every dollar
contributed, each person in the group receives $0.40, including the
contributor.
Imagine that you are playing the game, and you expect the other three
members of your group each to contribute $10. Then if you don’t
contribute, you will get $32 (three returns of $4 from their contributions,
plus the initial $20 that you keep). The others have paid $10, so they only
get $32 – $10 = $22 each. On the other hand, if you also contribute $10,
then everyone, including you, will get $22 + $4 = $26. Unfortunately for the
group, you do better by not contributing—that is, because the reward for
free riding ($32) is greater than for contributing ($26). And, unfortunately
for you, the same applies to each of the other members.
After each round, the participants are told the contributions of other
members of their group. In Figure 4.9a, each line represents the evolution
4.7 PUBLIC GOOD CONTRIBUTIONS AND PEER PUNISHMENT
153
over time of average contributions in a different location around the world.
Just as in the prisoners’ dilemma, people are definitely not solely self-
interested.
As you can see, players in Chengdu contributed $10 in the first round,
just as we described above. In every population where the game was played,
contributions to the public good were high in the first period, although
much more so in some cities (Copenhagen) than in others (Melbourne).
This is remarkable: if you care only about your own payoff, contributing
nothing at all is the dominant strategy. The high initial contributions could
have occurred because the participants in the experiment valued their
contribution to the payoffs that others received (they were altruistic). But
the difficulty (or, as Hardin would have described it, the tragedy) is obvious.
Everywhere, the contributions to the public good decreased over time.
In some cities this trend is very evident, for example, Copenhagen,
Bonn, or St. Gallen. In others (Muscat, Riyadh, or Athens), contributions are
still high at the end of the experiment, even though we would expect an
average contribution of $0. These results show a large variation across
societies in terms of contributions to the common pool.
The most plausible explanation of the pattern is not altruism. It is likely
that contributors decreased their level of cooperation if they observed that
others were contributing less than expected and were therefore free riding
on them. It seems as if those people who contributed more than the average
liked to punish the low contributors for their unfairness, or for violating a
social norm of contributing. Since the payoffs of free riders depend on the
total contribution to the public good, the only way to punish free riders in
this experiment was to stop contributing. This is the tragedy of the
commons.
Many people are happy to contribute as long as others reciprocate. A
disappointed expectation of reciprocity is the most convincing reason that
contributions fell so regularly in later rounds of this game.
To test this, the experimenters took the public goods game experiment
shown in Figure 4.9a and introduced a punishment option. After observing
the contributions of their group, individual players could pay to punish
other players by making them pay a $3 fine. The punisher remained
anonymous, but had to pay $1 per player punished. The effect is shown in
Figure 4.9b. For the majority of subjects, including those in China, South
0
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Dnipropetrovs'k
Minsk
St. Gallen
Muscat
Samara
Zurich
Boston
Bonn
Chengdu
Seoul
Riyadh
Nottingham
Athens
Istanbul
Melbourne
Figure 4.9a Worldwide public goods experiments: Contributions over 10 periods.
View this data at OWiD https://tinyco.re/
3562457
Benedikt Herrmann, Christian Thoni, and
Simon Gachter. 2008. ‘Antisocial
Punishment Across Societies’. Science
319 (5868): pp. 1362–67.
UNIT 4 SOCIAL INTERACTIONS
154
revealed preference A way of
studying preferences by reverse
engineering the motives of an indi-
vidual (her preferences) from
observations about her or his
actions.
Korea, northern Europe and the English-speaking countries, contributions
increased when they had the opportunity to punish free riders.
People who think that others have been unfair or have violated a social
norm may retaliate, even if the cost to themselves is high. Their punishment
of others is a form of altruism, because it costs them something to help
deter free riding behaviour that is detrimental to the wellbeing of most
members of the group.
This experiment illustrates the way that, even in large groups of people,
a combination of repeated interactions and social preferences can support
high levels of contribution to the public good.
The public goods game, like the prisoners’ dilemma, is a situation in
which there is something to gain for everyone by engaging with others in a
common project such as pest control, maintaining an irrigation system, or
controlling carbon emissions. But there is also something to lose when
others free ride.
•4.8 BEHAVIOURAL EXPERIMENTS IN THE LAB AND IN
THE FIELD
To understand economic behaviour, we need to know about people’s pref-
erences. In the previous unit, for example, students and farmers valued free
time. How much they valued it was part of the information we needed to
predict how much time they spend studying and farming.
In the past, economists have learned about our preferences from:
• Survey questions: To determine political preferences, brand loyalty,
degree of trust of others, or religious orientation.
• Statistical studies of economic behaviour: For example, purchases of one or
more goods when the relative price varies—to determine preferences for
the goods in question. One strategy is to reverse-engineer what the pref-
erences must have been, as revealed by purchases. This is called
revealed preference.
0
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1 2 3 4 5 6 7 8 9 10
Period
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Dnipropetrovs'k
Minsk
St. Gallen
Muscat
Samara
Zurich
Boston
Bonn
Chengdu
Seoul
Riyadh
Nottingham
Athens
Istanbul
Melbourne
Figure 4.9b Worldwide public goods experiments with opportunities for peer
punishment.
View this data at OWiD https://tinyco.re/
5283773
Benedikt Herrmann, Christian Thoni, and
Simon Gachter. 2008. ‘Antisocial
Punishment Across Societies’. Science
319 (5868): pp. 1362–67.
4.8 BEHAVIOURAL EXPERIMENTS IN THE LAB AND IN THE FIELD
155
In our ‘Economist in action’ video,
Juan Camilo Cárdenas talks about
his innovative use of experimental
economics in real-life situations.
https://tinyco.re/8801842
Surveys have a problem. Asking someone if they like ice cream will
probably get an honest answer. But the answer to the question: ‘How
altruistic are you?’ may be a mixture of truth, self-advertising, and wishful
thinking. Statistical studies cannot control the decision-making environ-
ment in which the preferences were revealed, so it is difficult to compare
the choices of different groups.
This is why economists sometimes use experiments, so that people’s
behaviour can be observed under controlled conditions.
HOW ECONOMISTS LEARN FROM FACTS
Laboratory experiments
Behavioural experiments have become important in the empirical study
of preferences. Part of the motivation for experiments is that under-
standing someone’s motivations (altruism, reciprocity, inequality
aversion as well as self-interest) is essential to being able to predict how
they will behave as employees, family members, custodians of the envir-
onment, and citizens.
Experiments measure what people do rather than what they say.
Experiments are designed to be as realistic as possible, while controlling
the situation:
• Decisions have consequences: The decisions in the experiment may
decide how much money the subjects earn by taking part. Sometimes
the stakes can be as high as a month’s income.
• Instructions, incentives and rules are common to all subjects: There is also
a common treatment. This means that if we want to compare two
groups, the only difference between the control and treatment groups
is the treatment itself, so that its effects can be identified.
• Experiments can be replicated: They are designed to be implementable
with other groups of participants.
• Experimenters attempt to control for other possible explanations: Other
variables are kept constant wherever possible, because they may
affect the behaviour we want to measure.
This means that when people behave differently in the experiment, it is
likely due to differences in their preferences, not in the situation that
each person faces.
Economists have studied public goods extensively using laboratory
experiments in which the subjects are asked to make decisions about
how much to contribute to a public good. In some cases, economists
have designed experiments that closely mimic real-world social
dilemmas. The work of Juan Camilo Cárdenas, an economist at the
Universidad de los Andes in Bogotá, Colombia is an example. He
performs experiments about social dilemmas with people who are facing
similar problems in their real life, such as overexploitation of a forest or
a fish stock. In our ‘Economist in action’ video he describes his use of
experimental economics in real-life situations, and how it helps us
understand why people cooperate even when there are apparent
incentives not to do so.
Economists have discovered that the way people behave in
experiments can be used to predict how they react in real-life situations.
UNIT 4 SOCIAL INTERACTIONS
156
Colin Camerer and Ernst Fehr.
2004. ‘Measuring Social Norms and
Preferences Using Experimental
Games: A Guide for Social
Scientists’. In Foundations of
Human Sociality: Economic
Experiments and Ethnographic
Evidence from Fifteen Small-Scale
Societies, edited by Joseph
Henrich, Robert Boyd, Samuel
Bowles, Colin Camerer, and
Herbert Gintis, Oxford: Oxford Uni-
versity Press.
Armin Falk and James J. Heckman.
2009. ‘Lab Experiments Are a Major
Source of Knowledge in the Social
Sciences’. Science 326 (5952):
pp. 535–538.
Joseph Henrich, Richard McElreath,
Abigail Barr, Jean Ensminger, Clark
Barrett, Alexander Bolyanatz, Juan
Camilo Cardenas, Michael Gurven,
Edwins Gwako, Natalie Henrich,
Carolyn Lesorogol, Frank Marlowe,
David Tracer, and John Ziker. 2006.
‘Costly Punishment Across Human
Societies’. Science 312 (5781):
pp. 1767–1770.
QUESTION 4.7 CHOOSE THE CORRECT ANSWER(S)
According to the ‘Economist in action’ video of Juan Camilo
Cárdenas (page 156), which of the following have economists
discovered using experiments simulating public goods scenarios?
The imposition of external regulation sometimes erodes the
willingness of participants to cooperate.
Populations with greater inequality exhibit a greater tendency to
cooperate.
Once real cash is used instead of tokens of hypothetical sums of
money, people cease to act cooperatively.
People are often willing to cooperate rather than free ride.
EXERCISE 4.5 ARE LAB EXPERIMENTS ALWAYS VALID?
In 2007, Steven Levitt and John List published a paper called ‘What Do
Laboratory Experiments Measuring Social Preferences Reveal about the
Real World?’ (https://tinyco.re/9601240). Read the paper to answer these
two questions.
1. According to their paper, why and how might people’s behaviour in
real life vary from what has been observed in laboratory experiments?
2. Using the example of the public goods experiment in this section,
explain why you might observe systematic differences between the
observations recorded in Figures 4.9a (page 154) and 4.9b (page 155),
and what might happen in real life.
Sometimes it is possible to conduct experiments ‘in the field’: that is, to
deliberately change the economic conditions under which people make
decisions, and observe how their behaviour changes. An experiment
conducted in Israel in 1998 demonstrated that social preferences may be
very sensitive to the context in which decisions are made.
It is common for parents to rush to pick up their children from daycare.
Sometimes a few parents are late, making teachers stay extra time. What
would you do to deter parents from being late? Two economists ran an
experiment introducing fines in some daycare centres but not others (these
For example, fishermen in Brazil who acted more cooperatively in an
experimental game also practiced fishing in a more sustainable manner
than the fishermen who were less cooperative in the experiment.
For a summary of the kinds of experiments that have been run, the
main results, and whether behaviour in the experimental lab predicts
real-life behaviour, read the research done by some of the economists
who specialize in experimental economics. For example, Colin Camerer
and Ernst Fehr, Armin Falk and James Heckman, or the experiments
done by Joseph Heinrich and a large team of collaborators around the
world.
In Exercise 4.5, however, Stephen Levitt and John List ask whether
people would behave the same way in the street as they do in the
laboratory.
Steven D. Levitt, and John A. List.
2007. ‘What Do Laboratory
Experiments Measuring Social Pref-
erences Reveal About the Real
World?’ Journal of Economic
Perspectives 21 (2): pp. 153–174.
4.8 BEHAVIOURAL EXPERIMENTS IN THE LAB AND IN THE FIELD
157
crowding out There are two quite distinct uses of the term. One
is the observed negative effect when economic incentives
displace people’s ethical or other-regarding motivations. In
studies of individual behaviour, incentives may have a
crowding out effect on social preferences. A second use of the
term is to refer to the effect of an increase in government
spending in reducing private spending, as would be expected
for example in an economy working at full capacity utilization,
or when a fiscal expansion is associated with a rise in the
interest rate.
were used as controls). The ‘price of lateness’ went from zero to ten Israeli
shekels (about $3 at the time). Surprisingly, after the fine was introduced,
the frequency of late pickups doubled. The top line in Figure 4.10
illustrates this.
Why did putting a price on lateness backfire?
One possible explanation is that before the fine was introduced, most
parents were on time because they felt that it was the right thing to do. In
other words, they came on time because of a moral obligation to avoid
inconveniencing the daycare staff. Perhaps they felt an altruistic concern
for the staff, or regarded a timely pick-up as a reciprocal responsibility in
the joint care of the child. But the imposition of the fine signalled that the
situation was really more like shopping. Lateness had a price and so could
be purchased, like vegetables or ice-cream.
The use of a market-like incentive—the price
of lateness—had provided what psychologists call
a new ‘frame’ for the decision, making it one in
which self-interest rather than concern for others
was acceptable. When fines and prices have these
unintended effects, we say that incentives have
crowded out social preferences. Even worse, you
can also see from Figure 4.10 that when the fine
was removed, parents continued to pick up their
children late.
Samuel Bowles. 2016. The Moral
Economy: Why Good Incentives
Are No Substitute for Good Cit-
izens. New Haven, CT: Yale
University Press.
Fines introduced Fines ended
0
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17
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Period
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Centres where fine introduced
Centres where fine not introduced
Figure 4.10 Average number of late-coming parents, per week.
Uri Gneezy and Aldo Rustichini. 2000. ‘A
Fine Is a Price’. The Journal of Legal
Studies 29 (January): pp. 1–17.
UNIT 4 SOCIAL INTERACTIONS
158
cooperation Participating in a
common project that is intended to
produce mutual benefits.
QUESTION 4.8 CHOOSE THE CORRECT ANSWER(S)
Figure 4.10 (page 158) depicts the average number of late-coming
parents per week in day-care centres, where a fine was introduced in
some centres and not in others. The fines were eventually abolished, as
indicated on the graph.
Based on this information, which of the following statements is
correct?
The introduction of the fine successfully reduced the number of
late-coming parents.
The fine can be considered as the ‘price’ for collecting a child.
The graph suggests that the experiment may have permanently
increased the parents’ tendency to be late.
The crowding out of the social preference did not occur until the
fines ended.
EXERCISE 4.6 CROWDING OUT
Imagine you are the mayor of a small town and wish to motivate your cit-
izens to get involved in ‘City Beautiful Day’, in which people spend one day
to help cleaning parks and roads.
How would you design the day to motivate citizens to take part?
••4.9 COOPERATION, NEGOTIATION, CONFLICTS OF
INTEREST, AND SOCIAL NORMS
Cooperation means participating in a common project in such a way that
mutual benefits occur. Cooperation need not be based on an agreement. We
have seen examples in which players acting independently can still achieve
a cooperative outcome:
• The invisible hand: Anil and Bala chose their crops in pursuit of their own
interests. Their engagement in the village market resulted in a mutually
beneficial division of labour.
• The repeated prisoners’ dilemma: They may refrain from using Terminator
for pest control because they recognize the future losses they would
suffer as a result of abandoning IPC.
• The public goods game: Players’ willingness to punish others sustained
high levels of cooperation in many countries, without the need for
agreements.
In other cases, such as the one-shot prisoners’ dilemma, independent
actions led to an unfortunate outcome. Then, the players could do better if
they could reach an agreement.
People commonly resort to negotiation to solve their economic and
social problems. For example, international negotiation resulted in the
Montreal Protocol, through which countries agreed to eliminate the use of
chlorofluorocarbons (CFCs), in order to avoid a harmful outcome (the
destruction of the ozone layer).
4.9 COOPERATION, NEGOTIATION, CONFLICTS OF INTEREST, AND SOCIAL NORMS
159
But negotiation does not always succeed, sometimes because of conflicts
of interest over how the mutual gains to cooperation will be shared. The
success of the Montreal Protocol contrasts with the relative failure of the
Kyoto Protocol in reducing carbon emissions responsible for global
warming. The reasons are partly scientific. The alternative technologies to
CFCs were well-developed and the benefits relative to costs for large indus-
trial countries, such as the US, were much clearer and larger than in the
case of greenhouse gas emissions. But one of the obstacles to agreement at
the Copenhagen climate change summit in 2009 was over how to share the
costs and benefits of limiting emissions between developed and developing
countries.
As a simpler example of a conflict of interest, consider a professor who
might be willing to hire a student as a research assistant for the summer. In
principle, both have something to gain from the relationship, because this
might also be a good opportunity for the student to earn some money and
learn. In spite of the potential for mutual benefit, there is also some room
for conflict. The professor may want to pay less and have more of his
research grant left over to buy a new computer, or he may need the work to
be done quickly, meaning the student can’t take time off. After negotiating,
they may reach a compromise and agree that the student can earn a small
salary while working from the beach. Or, perhaps, the negotiation will fail.
There are many situations like this in economics. A negotiation (some-
times called bargaining) is also an integral part of politics, foreign affairs,
law, social life and even family dynamics. A parent may give a child a
smartphone to play with in exchange for a quiet evening, a country might
consider giving up land in exchange for peace, or a government might be
willing to negotiate a deal with student protesters to avoid political
instability. As with the student and the professor, each of these bargains
might not actually happen if either side is not willing to do these things.
Negotiation: Sharing mutual gains
To help think about what makes a deal work, consider the following situ-
ation. You and a friend are walking down an empty street and you see a
$100 note on the ground. How would you decide how to split your lucky
find? If you split the amount equally, perhaps this reflects a social norm in
your community that says that something you get by luck should be split
50–50.
Dividing something of value in equal shares (the 50–50 rule) is a social
norm in many communities, as is giving gifts on birthdays to close family
members and friends. Social norms are common to an entire group of
people (almost all follow them) and tell a person what they should do in the
eyes of most people in the community.
In economics we think of people as making decisions according to their
preferences, by which we mean all of the likes, dislikes, attitudes, feelings,
and beliefs that motivate them. So everyone’s preferences are individual.
They may be influenced by social norms, but they reflect what people want
to do as well as what they think they ought to do.
We would expect that, even if there were a 50–50 norm in a community,
some individuals might not respect the norm exactly. Some people may act
more selfishly than the norm requires and others more generously. What
happens next will depend both on the social norm (a fact about the world,
which reflects attitudes to fairness that have evolved over long periods), but
also on the specific preferences of the individuals concerned.
UNIT 4 SOCIAL INTERACTIONS
160
fairness A way to evaluate an
allocation based on one’s
conception of justice.
Suppose the person who saw the money first has picked it up. There are
at least three reasons why that person might give some of it to a friend:
• Altruism: We have already considered this reason, in the case of Anil
and Bala. This person might be altruistic and care about the other being
happy, or about another aspect of the other’s wellbeing.
• Fairness: Or, the person holding the money might think that 50–50 is
fair. In this case, the person is motivated by fairness, or what economists
term inequality aversion.
• Reciprocity: The friend may have been kind to the lucky money-finder
in the past, or kind to others, and deserves to be treated generously
because of this. In this case we say that our money-finder has reciprocal
preferences.
These social preferences all influence our behaviour, sometimes working in
opposite directions. For example, if the money-finder has strong fairness
preferences but knows that the friend is entirely selfish, the fairness prefer-
ences tempt the finder to share but the reciprocity preferences push the
finder to keep the money.
QUESTION 4.9 CHOOSE THE CORRECT ANSWER(S)
Anastasia and Belinda’s favourite hobby is to go metal detecting. On
one occasion Anastasia finds four Roman coins while Belinda is
unsuccessful. Both women have reciprocal preferences. From this, can
we say that:
If both women are altruistic, then they will definitely share the find
50–50.
If Anastasia is altruistic and Belinda is selfish, then Anastasia may
not share the find.
If Anastasia is selfish and Belinda is altruistic, then Anastasia will
definitely not share the find.
If Anastasia is altruistic and Belinda believes in fairness, then they
may or may not share the find 50–50.
•4.10 DIVIDING A PIE (OR LEAVING IT ON THE TABLE)
One of the most common tools to study social preferences is a two-person
one-shot game known as the ultimatum game. It has been used around the
world with experimental subjects including students, farmers, warehouse
workers, and hunter-gatherers. By observing their choices we investigate
the subjects’ preferences and motives, such as pure self-interest, altruism,
inequality aversion, or reciprocity.
The subjects of the experiment are invited to play a game in which they
will win some money. How much they win will depend on how they and
the others in the game play. Real money is at stake in experimental games
like these, otherwise we could not be sure the subjects’ answers to a
hypothetical question would reflect their actions in real life.
The rules of the game are explained to the players. They are randomly
matched in pairs, then one player is randomly assigned as the Proposer, and
the other the Responder. The subjects do not know each other, but they
4.10 DIVIDING A PIE (OR LEAVING IT ON THE TABLE)
161
economic rent A payment or other
benefit received above and beyond
what the individual would have
received in his or her next best
alternative (or reservation option).
See also: reservation option.
know the other player was recruited to the experiment in the same way.
Subjects remain anonymous.
The Proposer is provisionally given an amount of money, say $100, by
the experimenter, and instructed to offer the Responder part of it. Any split
is permitted, including keeping it all, or giving it all away. We will call this
amount the ‘pie’ because the point of the experiment is how it will be
divided up.
The split takes the form: ‘x for me, y for you’ where x + y = $100. The
Responder knows that the Proposer has $100 to split. After observing the
offer, the Responder accepts or rejects it. If the offer is rejected, both indi-
viduals get nothing. If it is accepted, the split is implemented: the Proposer
gets x and the Responder y. For example, if the Proposer offers $35 and the
Responder accepts, the Proposer gets $65 and the Responder gets $35. If
the Responder rejects the offer, they both get nothing.
This is called a take-it-or-leave-it offer. It is the ultimatum in the game’s
name. The Responder is faced with a choice: accept $35, or get nothing.
This is a game about sharing the economic rents that arise in an
interaction. An entrepreneur wanting to introduce a new technology could
share the rent—the higher profit than is available from the current techno-
logy—with employees if they cooperate in its introduction. Here, the rent
arises because the experimenter provisionally gives the Proposer the pie to
divide. If the negotiation succeeds (the Responder accepts), both players
receive a rent (a slice of the pie); their next best alternative is to get nothing
(the pie is thrown away).
In the example above, if the Responder accepts the Proposer’s offer, then
the Proposer gets a rent of $65, and the Responder gets $35. For the
Responder there is a cost to saying no. He loses the rent that he would have
received. Therefore $35 is the opportunity cost of rejecting the offer.
We start by thinking about a simplified case of the ultimatum game,
represented in Figure 4.11 in a diagram called a ‘game tree’. The Proposer’s
choices are either the ‘fair offer’ of an equal split, or the ‘unfair offer’ of 20
(keeping 80 for herself). Then the respondent has the choice to accept or
reject. The payoffs are shown in the last row.
Proposer
Responder Responder
Offer
(50, 50)
Accept
(50, 50)
Reject
(0, 0)
Accept
(80, 20)
Reject
(0, 0)
Offer
(80, 20)
Figure 4.11 Game tree for the ultimatum game.
UNIT 4 SOCIAL INTERACTIONS
162
sequential game A game in which
all players do not choose their
strategies at the same time, and
players that choose later can see
the strategies already chosen by
the other players, for example the
ultimatum game. See also:
simultaneous game.
simultaneous game A game in
which players choose strategies
simultaneously, for example the
prisoners’ dilemma. See also:
sequential game.
minimum acceptable offer In the
ultimatum game, the smallest offer
by the Proposer that will not be
rejected by the Responder.
Generally applied in bargaining
situations to mean the least
favourable offer that would be
accepted.
The game tree is a useful way to represent social interactions because it
clarifies who does what, when they choose, and what are the results. We see
that in the ultimatum game one player (the Proposer) chooses her strategy
first, followed by the Responder. It is called a sequential game; previously
we looked at simultaneous games, in which players chose strategies
simultaneously.
What the Proposer will get depends on what the Responder does, so the
Proposer has to think about the likely response of the other player. That is
why this is called a strategic interaction. If you’re the Proposer you can’t try
out a low offer to see what happens: you have only one chance to make an
offer.
Put yourself in the place of the Responder in this game. Would you
accept (50, 50)? Would you accept (80, 20)? Now switch roles. Suppose that
you are the Proposer. What split would you offer to the Responder? Would
your answer depend on whether the other person was a friend, a stranger, a
person in need, or a competitor? A Responder who thinks that the
Proposer’s offer has violated a social norm of fairness, or that the offer is
insultingly low for some other reason, might be willing to sacrifice the
payoff to punish the Proposer.
Now return to the general case, in which the Proposer can offer any
amount between $0 and $100. If you were the Responder, what is the
minimum amount you would be willing to accept? If you were the
Proposer, what would you offer?
If you work through the Einstein below, and Exercise 4.7 that follows it,
you will see how to work out the minimum acceptable offer, taking
account of the social norm and of the individual’s own attitude to
reciprocity. The minimal acceptable offer is the offer at which the pleasure
of getting the money is equal to the satisfaction the person would get from
refusing the offer and getting no money, but being able to punish the
Proposer for violating the social norm of 50–50. If you are the Responder
and your minimum acceptable offer is $35 (of the total pie of $100) then, if
the Proposer offered you $36, you might not like the Proposer much, but
you would still accept the offer instead of punishing the Proposer by
rejecting the offer. If you rejected the offer, you would go home with
satisfaction worth $35 and no money, when you could have had $36 in
cash.
EINSTEIN
When will an offer in the ultimatum game be accepted?
Suppose $100 is to be split, and there is a fairness norm of 50–50. When
the proposal is $50 or above, (y ≥ 50), the Responder feels positively
disposed towards the Proposer and would naturally accept the proposal,
as rejecting it would hurt both herself and the Proposer whom she
appreciates because they conform to, or were even more generous than,
the social norm. But if the offer is below $50 then she feels that the
50–50 norm is not being respected, and she may want to punish the
Proposer for this breach. If she does reject the offer, this will come at a
cost to her, because rejection means that both receive nothing.
Suppose the Responder’s anger at the breach of the social norm
depends on the size of the breach: if the Proposer offers nothing she will
be furious, but she’s more likely to be puzzled than angry at an offer of
4.10 DIVIDING A PIE (OR LEAVING IT ON THE TABLE)
163
$49.50 rather than the $50 offer she might have expected based on the
social norm. So how much satisfaction she would derive from punishing
a Proposer’s low offer depends on two things: her private reciprocity
motive (R), and the gain from accepting the offer (y). R is a number that
indicates the strength of the Responder’s private reciprocity motive: if R
is a large number, then she cares a lot about whether the Proposer is
acting generously and fairly or not, but if R = 0 she does not care about
the Proposer’s motives at all. So the satisfaction at rejecting a low offer is
R(50 – y). The gain from accepting the offer is the offer itself, or y.
The decision to accept or reject just depends on which of these two
quantities is larger. We can write this as ‘reject an offer if y < R(50 − y)’.
This equation says that she will reject an offer of less than $50 according
to how much lower than $50 the offer is (as measured by (50 − y)),
multiplied by her private attitude to reciprocity (R).
To calculate her minimum acceptable offer we can rearrange this
rejection equation like this:
R = 1 means that the Responder places equal importance on reciprocity
and the social norm. When R = 1, then y < 25 and she will reject any
offer less than $25. The cutoff point of $25 is where her two motivations
of monetary gain and punishing the Proposer exactly balance out: if she
rejects the offer of $25, she loses $25 but receives $25 worth of
satisfaction from punishing the Proposer so her total payoff is $0.
The more the Responder cares about reciprocity, the higher the
Proposer’s offers have to be. For example, if R = 0.5, the Responder will
reject offers below $16.67 (y < 16.67), but if R = 2, then the Responder
will reject any offer less than $33.33.
EXERCISE 4.7 ACCEPTABLE OFFERS
1. How might the minimum acceptable offer depend on the method by
which the Proposer acquired the $100 (for example, did she find it on
the street, win it in the lottery, receive it as an inheritance, and so on)?
2. Suppose that the fairness norm in this society is 50–50. Can you imagine
anyone offering more than 50% in such a society? If so, why?
UNIT 4 SOCIAL INTERACTIONS
164
•4.11 FAIR FARMERS, SELF-INTERESTED STUDENTS?
If you are a Responder in the ultimatum game who cares only about your
own payoffs, you should accept any positive offer because something, no
matter how small, is always better than nothing. Therefore, in a world
composed only of self-interested individuals, the Proposer would anticipate
that the Responder would accept any offer and, for that reason, would offer
the minimum possible amount—one cent—knowing it would be accepted.
Does this prediction match the experimental data? No, it does not. As in
the prisoners’ dilemma, we don’t see the outcome we would predict if
people were entirely self-interested. One-cent offers get rejected.
To see how farmers in Kenya and students in the US played this game,
look at Figure 4.12. The height of each bar indicates the fraction of
Responders who were willing to accept the offer indicated on the hori-
zontal axis. Offers of more than half of the pie were acceptable to all of the
subjects in both countries, as you would expect.
Notice that the Kenyan farmers are very unwilling to accept low offers,
presumably regarding them as unfair, while the US students are much more
willing to do so. For example, virtually all (90%) of the farmers would say
no to an offer of one-fifth of the pie (the Proposer keeping 80%), while 63%
of the students would accept such a low offer. More than half of the
students would accept just 10% of the pie, but almost none of the farmers
would.
Although the results in Figure 4.12 indicate that attitudes differ towards
what is fair, and how important fairness is, nobody in the Kenyan and US
experiments was willing to accept an offer of zero, even though by rejecting
it they would also receive zero.
This is not always the case. In
experiments in Papua New Guinea
offers of more than half of the pie
were commonly rejected by
Responders who preferred to
receive nothing than to participate
in a very unequal outcome even if
it was in the Responder’s favour, or
to incur the social debt of having
received a large gift that might be
difficult to reciprocate. The
subjects were inequity averse,
even if the inequality in question
benefited them.
Joseph Henrich, Robert Boyd,
Samuel Bowles, Colin Camerer,
and Herbert Gintis (editors). 2004.
Foundations of Human Sociality:
Economic Experiments and
Ethnographic Evidence from
Fifteen Small-Scale Societies.
Oxford: Oxford University Press.
0
25
50
75
100
0 10 20 30 40 50
Fraction of the pie offered by the Proposer to the Responder (%)
Sh
ar
e
of
Re
sp
on
de
rs
w
ho
w
ou
ld
ac
ce
pt
th
e
off
er
(%
)
Farmers (Kenya)
Students, Emory University (US)
Figure 4.12 Acceptable offers in the ultimatum game.
Adapted from Joseph Henrich, Richard
McElreath, Abigail Barr, Jean Ensminger,
Clark Barrett, Alexander Bolyanatz, Juan
Camilo Cardenas, Michael Gurven,
Edwins Gwako, Natalie Henrich, Carolyn
Lesorogol, Frank Marlowe, David Tracer,
and John Ziker. 2006. ‘Costly Punishment
Across Human Societies’. Science 312
(5781): pp. 1767–1770.
4.11 FAIR FARMERS, SELF-INTERESTED STUDENTS?
165
EXERCISE 4.8 SOCIAL PREFERENCES
Consider the experiment described in Figure 4.12 (page 165):
1. Which of the social preferences discussed above do you think
motivated the subjects’ willingness to reject low offers, even though by
doing so they would receive nothing at all?
2. Why do you think that the results differed between the Kenyan farmers
and the US students?
3. What responses would you expect if you played this game with two dif-
ferent sets of players—your classmates and your family? Explain
whether or not you expect the results to differ across these groups. If
possible, play the game with your classmates and your family and
comment on whether the results are consistent with your predictions.
The full height of each bar in Figure 4.13 indicates the percentage of the
Kenyan and American Proposers who made the offer shown on the hori-
zontal axis. For example, half of the farmers made proposals of 40%.
Another 10% offered an even split. Only 11% of the students made such
generous offers.
Students, Emory University (US) (darker shading shows the proportion of offers expected to be rejected)
Farmers (Kenya) (darker shading shows the proportion of offers expected to be rejected)
Half of the Kenyan farmer
proposers made an offer of 40%
Kenyan farmer Responders
are expected to reject a
30% offer 48% of the time
Kenyan farmer Responders
are expected to reject a
40% offer 4% of the time
0
15
30
45
60
0 10 20 30 40 50
Fraction of the pie offered by the Proposer to the Responder (%)
Sh
ar
e
of
th
e
Pr
op
os
er
s
m
ak
in
g
th
e
off
er
in
di
ca
te
d
(%
)
Figure 4.13 Actual offers and expected rejections in the ultimatum game.
Adapted from Joseph Henrich, Richard
McElreath, Abigail Barr, Jean Ensminger,
Clark Barrett, Alexander Bolyanatz, Juan
Camilo Cardenas, Michael Gurven,
Edwins Gwako, Natalie Henrich, Carolyn
Lesorogol, Frank Marlowe, David Tracer,
and John Ziker. 2006. ‘Costly Punishment
Across Human Societies’. Science 312
(5781): pp. 1767–1770.
1. What do the bars show?
The full height of each bar in the figure
indicates the percentage of the Kenyan
and American Proposers who made the
offer shown on the horizontal axis.
2. Reading the figure
For example: for Kenyan farmers, 50%
on the vertical axis and 40% on the
horizontal axis means half of the
Kenyan Proposers made an offer of
40%.
3. The dark-shaded area shows
rejections
If Kenyan farmers made an offer of
30%, almost half of Responders would
reject it. (The dark part of the bar is
almost as big as the light part.)
4. Better offers, fewer rejections
The relative size of the dark area is
smaller for better offers: for example
Kenyan farmer Responders rejected a
40% offer only 4% of the time.
UNIT 4 SOCIAL INTERACTIONS
166
But were the farmers really generous? To answer, you have to think not
only about how much they were offering, but also what they must have
reasoned when considering whether the Respondent would accept the
offer. If you look at Figure 4.13 and concentrate on the Kenyan farmers,
you will see that very few proposed to keep the entire pie by offering zero
(4% of them as shown in the far left-hand bar) and all of those offers would
have been rejected (the entire bar is dark).
On the other hand, looking at the far right of the figure, we see that for
the farmers, making an offer of half the pie ensured an acceptance rate of
100% (the entire bar is light). Those who offered 30% were about equally
likely to see their offer rejected as accepted (the dark part of the bar is
nearly as big as the light part).
A Proposer who wanted to earn as much as possible would choose
something between the extreme of trying to take it all or dividing it equally.
The farmers who offered 40% were very likely to see their offer accepted
and receive 60% of the pie. In the experiment, half of the farmers chose an
offer of 40%. We would expect the offer to be rejected only 4% of the time,
as can be seen from the dark-shaded part of the bar at the 40% offer in
Figure 4.13.
Now suppose you are a Kenyan farmer and all you care about is your
own payoff.
Offering to give the Responder nothing is out of the question because
that will ensure that you get nothing when they reject your offer. Offering
half will get you half for sure—because the respondent will surely accept.
But you suspect that you can do better.
A Proposer who cares only about his own payoffs will compare what is
called the expected payoffs of the two offers: that is, the payoff that one may
expect, given what the other person is likely to do (accept or reject) in case
this offer is made. Your expected payoff is the payoff you get if the offer is
accepted, multiplied by the probability that it will be accepted (remember
that if the offer is rejected, the Proposer gets nothing). Here is how the
Proposer would calculate the expected payoffs of offering 40% or 30%:
We cannot know if the farmers actually made these calculations, of course.
But if they did, they would have discovered that offering 40% maximized
their expected payoff. This motivation contrasts with the case of the
acceptable offers in which considerations of inequality aversion,
reciprocity, or the desire to uphold a social norm were apparently at work.
Unlike the Responders, many of the Proposers may have been trying to
make as much money as possible in the experiment and had guessed
correctly what the Responders would do.
Similar calculations indicate that, among the students, the expected
payoff-maximizing offer was 30%, and this was the most common offer
among them. The students’ lower offers could be because they correctly
4.11 FAIR FARMERS, SELF-INTERESTED STUDENTS?
167
anticipated that lowball offers (even as low as 10%) would sometimes be
accepted. They may have been trying to maximize their payoffs and hoping
that they could get away with making low offers.
EXERCISE 4.9 OFFERS IN THE ULTIMATUM GAME
1. Why do you think that some of the farmers offered more than 40%?
Why did some of the students offer more than 30%?
2. Why did some offer less than 40% (farmers) and 30% (students)?
3. Which of the social preferences that you have studied might help to
explain the results shown?
How do the two populations differ? Although many of the farmers and the
students offered an amount that would maximize their expected payoffs,
the similarity ends there. The Kenyan farmers were more likely to reject
low offers. Is this a difference between Kenyans and Americans, or between
farmers and students? Or is it something related to local social norms,
rather than nationality and occupation? Experiments alone cannot answer
these interesting questions, but before you jump to the conclusion that
Kenyans are more averse to unfairness than Americans, when the same
experiment was run with rural Missourians in the US, they were even more
likely to reject low offers than the Kenyan farmers. Almost every
Missourian Proposer offered half the pie.
QUESTION 4.10 CHOOSE THE CORRECT ANSWER(S)
Consider an ultimatum game where the Proposer offers a proportion
of $100 to the Responder, who can either accept or reject the offer. If
the Responder accepts, both the Proposer and the Responder keep the
agreed share, while if the Responder rejects, then both receive
nothing. Figure 4.12 (page 165) shows the results of a study that
compares the responses of US university students and Kenyan farmers.
From this information, we can conclude that:
Kenyans are more likely to reject low offers than Americans.
Just over 50% of Kenyan farmers rejected the offer of the Proposer
keeping 30%.
Both groups of Responders are indifferent between accepting and
rejecting an offer of receiving nothing.
Kenyan farmers place higher importance on fairness than US
students.
UNIT 4 SOCIAL INTERACTIONS
168
QUESTION 4.11 CHOOSE THE CORRECT ANSWER(S)
The following table shows the percentage of the Responders who
rejected the amount offered by the Proposers in the ultimatum game
played by Kenyan farmers and US university students. The pie is $100.
Amount offered $0 $10 $20 $30 $40 $50
Kenyan
farmers
100% 100% 90% 48% 4% 0%
Proportion
rejected
US students 100% 40% 35% 15% 10% 0%
From this information, we can say that:
The expected payoff of offering $30 is $4.50 for the US students.
The expected payoff of offering $40 is $6 for the US students.
The expected payoff of offering $20 is $8 for the Kenyan farmers.
The expected payoff of offering $10 is higher for the Kenyan farm-
ers than for the US students.
EXERCISE 4.10 STRIKES AND THE ULTIMATUM GAME
A strike over pay or working conditions may be considered an example of
an ultimatum game.
1. To model a strike as an ultimatum game, who is the Proposer and who
is the Responder?
2. Draw a game tree to represent the situation between these two parties.
3. Research a well-known strike and explain how it satisfies the definition
of an ultimatum game.
4. In this section, you have been presented with experimental data on
how people play the ultimatum game. How could you use this informa-
tion to suggest what kind of situations might lead to a strike?
4.12 COMPETITION IN THE ULTIMATUM GAME
Ultimatum game experiments with two players suggest how people may
choose to share the rent arising from an economic interaction. But the out-
come of a negotiation may be different if it is affected by competition. For
example, the professor looking for a research assistant could consider
several applicants rather than just one.
Imagine a new version of the ultimatum game in which a Proposer
offers a two-way split of $100 to two respondents, instead of just one. If
either of the Responders accepts but not the other, that Responder and the
Proposer get the split, and the other Responder gets nothing. If no one
accepts, no one gets anything, including the Proposer. If both Responders
accept, one is chosen at random to receive the split.
If you are one of the Responders, what is the minimum offer you would
accept? Are your answers any different, compared to the original ultimatum
game with a single Responder? Perhaps. If I knew that my fellow
competitor is strongly driven by 50–50 split norms, my answer would not
be too different. But what if I suspect that my competitor wants the reward
very much, or does not care too much about how fair the offer is?
And now suppose you are the Proposer. What split would you offer?
4.12 COMPETITION IN THE ULTIMATUM GAME
169
Figure 4.14 shows some laboratory evidence for a large group of subjects
playing multiple rounds. Proposers and Responders were randomly and
anonymously matched in each round.
The red bars show the fraction of offers that are rejected when there is a
single Responder. The blue bars show what happens with two Responders.
When there is competition, Responders are less likely to reject low offers.
Their behaviour is more similar to what we would expect of self-interested
individuals concerned mostly about their own monetary payoffs.
To explain this phenomenon to yourself, think about what happens
when a Responder rejects a low offer. This means getting a zero payoff.
Unlike the situation in which there is a sole Responder, the Responder in a
competitive situation cannot be sure the Proposer will be punished, because
the other Responder may accept the low offer (not everyone has the same
norms about proposals, or is in the same state of need).
Consequently, even fair-minded people will accept low offers to avoid
having the worst of both worlds. Of course, the Proposers also know this,
so they will make lower offers, which Responders still accept. Notice how a
small change in the rules or the situation can have a big effect on the out-
come. As in the public goods game where the addition of an option to
punish free riders greatly increased the levels of contribution, changes in
the rules of the game matter.
0
25
50
75
100
0 5 10 15 20 25 30 35 40 45 50
Fraction of the pie offered by the Proposer to the Responder(s) (%)
Sh
ar
e
of
off
er
s
re
je
ct
ed
(%
) One ResponderTwo Responders
Figure 4.14 Fraction of offers rejected in the ultimatum game, according to offer
size and the number of Responders.
Adapted from Figure 6 in Urs
Fischbacher, Christina M. Fong, and Ernst
Fehr. 2009. ‘Fairness, Errors and the
Power of Competition’. Journal of Eco-
nomic Behavior & Organization 72 (1):
pp. 527–45.
UNIT 4 SOCIAL INTERACTIONS
170
Nash equilibrium A set of
strategies, one for each player in
the game, such that each player’s
strategy is a best response to the
strategies chosen by everyone else.
EXERCISE 4.11 A SEQUENTIAL PRISONERS’ DILEMMA
Return to the prisoners’ dilemma pest control game that Anil and Bala
played in Figure 4.3b (page 142), but now suppose that the game is played
sequentially, like the ultimatum game. One player (chosen randomly)
chooses a strategy first (the first mover), and then the second moves (the
second mover).
1. Suppose you are the first mover and you know that the second mover
has strong reciprocal preferences, meaning the second mover will act
kindly towards someone who upholds social norms not to pollute and
will act unkindly to someone who violates the norm. What would you
do?
2. Suppose the reciprocal person is now the first mover interacting with
the person she knows to be entirely self-interested. What do you think
would be the outcome of the game?
••••4.13 SOCIAL INTERACTIONS: CONFLICTS IN THE
CHOICE AMONG NASH EQUILIBRIA
In the invisible hand game, the prisoners’ dilemma, and the public goods
game, the action that gave a player the highest payoffs did not depend on
what the other player did. There was a dominant strategy for each player,
and hence a single dominant strategy equilibrium.
But this is often not the case.
We have already mentioned a situation in which it is definitely untrue.
Driving on the right or on the left. If others drive on the right, your best
response is to drive on the right too. If they drive on the left, your best
response is to drive on the left.
In the US, everyone driving on the right is an equilibrium, in the sense
that no one would want to change their strategy given what others are
doing. In game theory, if everyone is playing their best response to the
strategies of everyone else, these strategies are termed a Nash equilibrium.
In Japan, though, Drive on the Left is a Nash equilibrium. The driving
‘game’ has two Nash equilibria.
Many economic interactions do not have dominant strategy equilibria,
but if we can find a Nash equilibrium, it gives us a prediction of what we
should observe. We should expect to see all players doing the best they can,
given what others are doing.
But even in simple economic problems there may be more than one
Nash equilibrium (as in the driving game). Suppose that when Bala and Anil
choose their crops the payoffs are as shown in Figure 4.15. This is different
from the invisible hand game. If the two farmers produce the same crop,
there is now such a large fall in price that it is better for each to specialize,
even in the crop they are less suited to grow. Follow the steps in Figure 4.15
to find the two equilibria.
Situations with two Nash equilibria prompt us to ask two questions:
• Which equilibrium would we expect to observe in the world?
• Is there a conflict of interest because one equilibrium is preferable to
some players, but not to others?
4.13 SOCIAL INTERACTIONS: CONFLICTS IN THE CHOICE AMONG NASH EQUILIBRIA
171
Whether you drive on the right or the left is not a matter of conflict in itself,
as long as everyone you are driving towards has made the same decision as
you. We can’t say that driving on the left is better than driving on the right.
But in the division of labour game, it is clear that the Nash equilibrium
with Anil choosing Cassava and Bala choosing Rice (where they specialize
in the crop they produce best) is preferred to the other Nash equilibrium by
both farmers.
Could we say, then, that we would expect to see Anil and Bala engaged in
the ‘correct’ division of labour? Not necessarily. Remember, we are
assuming that they take their decisions independently, without
coordinating. Imagine that Bala’s father had been especially good at
growing cassava (unlike his son) and so the land remained dedicated to
cassava even though it was better suited to producing rice. In response to
this, Anil knows that Rice is his best response to Bala’s Cassava, and so
would have then chosen to grow rice. Bala would have no incentive to
switch to what he is good at: growing rice.
The example makes an important point. If there is more than one Nash
equilibrium, and if people choose their actions independently, then an eco-
nomy can get ‘stuck’ in a Nash equilibrium in which all players are worse
off than they would be at the other equilibrium.
Rice Cassava
Bala
1
0
2
2
4
4
0
1Ca
ss
av
a
Ri
ce
An
il
Figure 4.15 A division of labour problem with more than one Nash equilibrium.
1. Anil’s best response to Rice
If Bala is going to choose Rice, Anil’s
best response is to choose Cassava. We
place a dot in the bottom left-hand
cell.
2. Anil’s best response to Cassava
If Bala is going to choose Cassava,
Anil’s best response is to choose Rice.
Place a dot in the top right-hand cell.
Notice that Anil does not have a
dominant strategy.
3. Bala’s best responses
If Anil chooses Rice, Bala’s best
response is to choose Cassava, and if
Anil chooses Cassava he should choose
Rice. The circles show Bala’s best
responses. He doesn’t have a dominant
strategy either.
4. (Cassava, Rice) is a Nash equilibrium
If Anil chooses Cassava and Bala
chooses Rice, both of them are playing
best responses (a dot and a circle
coincide). So this is a Nash equilibrium.
5. (Rice, Cassava) is also a Nash
equilibrium
If Anil chooses Rice and Bala chooses
Cassava then both of them are playing
best responses, so this is also a Nash
equilibrium, but the payoffs are higher
in the other equilibrium.
UNIT 4 SOCIAL INTERACTIONS
172
GREAT ECONOMISTS
John Nash
John Nash (1928–2015) completed
his doctoral thesis at Princeton
University at the age of 21. It was
just 27 pages long, yet it advanced
game theory (which was a little-
known branch of mathematics
back then) in ways that led to a
dramatic transformation of eco-
nomics. He provided an answer to
the question: when people interact
strategically, what would one
expect them to do? His answer,
now known as a Nash equilib-
rium, is a collection of strategies, one for each player, such that if these
strategies were to be publicly revealed, no player would regret his or her
own choice. That is, if all players choose strategies that are consistent
with a Nash equilibrium, then nobody can gain by unilaterally switching
to a different strategy.
Nash did much more than simply introduce the concept of an equi-
librium, he proved that such an equilibrium exists under very general
conditions, provided that players are allowed to randomize over their
available set of strategies. To see the importance of this, consider the
two-player children’s game rock-paper-scissors. If each of the players
picks one of the three strategies with certainty, then at least one of the
players would be sure to lose and would therefore have been better off
choosing a different strategy. But if both players choose each available
strategy with equal probability, then neither can do better by
randomizing over strategies in a different way. This is accordingly a
Nash equilibrium.
What Nash was able to prove is that any game with a finite number of
players, each of whom has a finite number of strategies, must have at
least one equilibrium, provided that players can randomize freely. This
result is useful because strategies can be very complicated objects,
specifying a complete plan that determines what action is to be taken in
any situation that could possibly arise. The number of distinct strategies
in chess, for instance, is greater than the number of atoms in the known
universe. Yet we know that chess has a Nash equilibrium, although it
remains unknown whether the equilibrium involves a win for white, a
win for black, or a guaranteed draw.
What was remarkable about Nash’s existence proof is that some of
the most distinguished mathematicians of the twentieth century, includ-
ing Emile Borel and John von Neumann, had tackled the problem
without getting very far. They were able to show the existence of equi-
librium only for certain zero-sum games; those in which the gain for one
player equals the loss to the others. This clearly limited the scope of their
theory for economic applications. Nash allowed for a much more
general class of games, where players could have any goals whatsoever.
They could be selfish, altruistic, spiteful, or fair-minded, for instance.
4.13 SOCIAL INTERACTIONS: CONFLICTS IN THE CHOICE AMONG NASH EQUILIBRIA
173
Sylvia Nasar. 2011. A Beautiful
Mind: The Life of Mathematical
Genius and Nobel Laureate John
Nash. New York, NY: Simon &
Schuster.
Resolving conflict
A conflict of interest occurs if players in a game would prefer different
Nash equilibria.
To see this, consider the case of Astrid and Bettina, two software
engineers who are working on a project for which they will be paid. Their
first decision is whether the code should be written in Java or C++ (imagine
that either programming language is equally suitable, and that the project
can be written partly in one language and partly in the other). They each
have to choose one program or the other, but Astrid wants to write in Java
because she is better at writing Java code. While this is a joint project with
Bettina, her pay will be partly based on how many lines of code were
written by her. Unfortunately Bettina prefers C++ for just the same reason.
So the two strategies are called Java and C++.
Their interaction is described in Figure 4.16a, and their payoffs are in
Figure 4.16b.
From Figure 4.16a, you can work out three things:
• They both do better if they work in the same language.
• Astrid does better if that language is Java, while the reverse is true for
Bettina.
• Their total payoff is higher if they choose C++.
How would we predict the outcome of this game?
If you use the dot-and-circle method, you will find that each player’s best
responses are to choose the same language as the other player. So there are
two Nash equilibria. In one, both choose Java. In the other, both choose
C++.
There is hardly a field in economics that the development of game
theory has not completely transformed, and this development would
have been impossible without Nash’s equilibrium concept and existence
proof. Remarkably, this was not Nash’s only path-breaking contribution
to economics—he also made a brilliantly original contribution to the
theory of bargaining. In addition, he made pioneering contributions to
other areas of mathematics, for which he was awarded the prestigious
Abel Prize.
Nash would go on to share the Nobel Prize for his work. Roger
Myerson, an economist who also won the prize, described the Nash
equilibrium as ‘one of the most important contributions in the history of
economic thought.’
Nash originally wanted to be an electrical engineer like his father,
and studied mathematics as an undergraduate at Carnegie Tech (now
Carnegie-Mellon University). An elective course in International Eco-
nomics stirred his interest in strategic interactions, which eventually led
to his breakthrough.
For much of his life Nash suffered from mental illness that required
hospitalization. He experienced hallucinations caused by schizophrenia
that began in 1959, though after what he described as ‘25 years of
partially deluded thinking’ he continued his teaching and research at
Princeton. The story of his insights and illness are told in the book
(made into a film starring Russell Crowe) A Beautiful Mind.
UNIT 4 SOCIAL INTERACTIONS
174
Can we say which of these two equilibria is more likely to occur? Astrid
obviously prefers that they both play Java while Bettina prefers that they
both play C++. With the information we have about how the two might
interact, we can’t yet predict what would happen. Exercise 4.12 gives some
examples of the type of information that would help to clarify what we
would observe.
Both work in the
same language
Astrid benefits more:
she is better at
Java coding
Each is working in the
language they are
better at
But working in different
languages is less productive
than if both work in the
same language
Each is working in the
language they are less good at,
and so neither works fast
Working in different
languages is
less productive
Both work in the
same language
Bettina benefits more:
she is better at
C++ coding
C++Java
Bettina
As
tr
id
C+
+
Ja
va
Figure 4.16a Interactions in the choice of programming language.
Java C++
Bettina
3
4
2
2
0
0
6
3
As
tr
id
Ja
va
C+
+
Figure 4.16b Payoffs (thousands of dollars to complete the project) according to
the choice of programming language.
4.13 SOCIAL INTERACTIONS: CONFLICTS IN THE CHOICE AMONG NASH EQUILIBRIA
175
EXERCISE 4.12 CONFLICT BETWEEN ASTRID AND BETTINA
What is the likely result of the game in Figure 4.16b (page 175) if:
1. Astrid can choose which language she will use first, and commit to it
(just as the Proposer in the ultimatum game commits to an offer, before
the Responder responds)?
2. The two can make an agreement, including which language they use,
and how much cash can be transferred from one to the other?
3. They have been working together for many years, and in the past they
used Java on joint projects?
EXERCISE 4.13 CONFLICT IN BUSINESS
In the 1990s, Microsoft battled Netscape over market share for their web
browsers, called Internet Explorer and Navigator. In the 2000s, Google and
Yahoo fought over which company’s search engine would be more
popular. In the entertainment industry, a battle called the ‘format wars’
played out between Blu-Ray and HD-DVD.
Use one of these examples to analyse whether there are multiple
equilibria and, if so, why one equilibrium might emerge in preference to
the others.
QUESTION 4.12 CHOOSE THE CORRECT ANSWER(S)
This table shows the payoff matrix for a simultaneous one-shot game
in which Anil and Bala choose their crops.
Rice Cassava
Bala
1
0
2
2
4
4
0
1Ca
ss
av
a
Ri
ce
An
il
We can conclude that:
There are two Nash equilibria: (Cassava, Rice) and (Rice, Cassava).
The choice of Cassava is a dominant strategy for Anil.
The choice of Rice is a dominant strategy for Bala.
There are two dominant strategy equilibria: (Cassava, Rice) and
(Rice, Cassava).
UNIT 4 SOCIAL INTERACTIONS
176
EXERCISE 4.14 NASH EQUILIBRIA AND CLIMATE
CHANGE
Think of the problem of climate change as a game
between two countries called China and the US, con-
sidered as if each were a single individual. Each country
has two possible strategies for addressing global
carbon emissions: Restrict (taking measures to reduce
emissions, for example by taxing the use of fossil fuels)
and BAU (the Stern report’s business as usual scenario).
Figure 4.17 describes the outcomes (top) and
hypothetical payoffs (bottom), on a scale from best,
through good and bad, to worst. This is called an
ordinal scale (because all that matters is the order:
whether one outcome is better than the other, and not
by how much it is better).
Reduction in
emissions sufficient
to moderate
climate change
US free rides on
Chinese emissions
cutbacks
No reduction
in emissions
China free rides on
US emissions
cutbacks
Restrict BAU
US
Ch
in
a
BA
U
Re
st
ri
ct
Restrict BAU
US
GOOD
GOOD
BEST
WORST
WORST
BEST
BAD
BAD
Ch
in
a
BA
U
Re
st
ri
ct
Restrict BAU
US
BEST
BEST
GOOD
WORST
WORST
GOOD
BAD
BAD
Ch
in
a
BA
U
Re
st
ri
ct
Figure 4.17 Climate change policy as a prisoners’ dilemma (top). Payoffs for a
climate change policy as a prisoners’ dilemma (bottom left), and payoffs with
inequality aversion and reciprocity (bottom right).
1. Show that both countries have a dominant strategy.
What is the dominant strategy equilibrium?
2. The outcome would be better for both countries if
they could negotiate a binding treaty to restrict
emissions. Why might it be difficult to achieve this?
3. Explain how the payoffs in the bottom right of Figure
4.17 could represent the situation if both countries
were inequality averse and motivated by reciprocity.
Show that there are two Nash equilibria. Would it be
easier to negotiate a treaty in this case?
4. Describe the changes in preferences or in some
other aspect of the problem that would convert the
game to one in which (like the invisible hand game)
both countries choosing Restrict is a dominant
strategy equilibrium.
4.13 SOCIAL INTERACTIONS: CONFLICTS IN THE CHOICE AMONG NASH EQUILIBRIA
177
4.14 CONCLUSION
We have used game theory to model social interactions. The invisible hand
game illustrates how markets may channel individual self-interest to
achieve mutual benefits, but the dominant strategy equilibrium of the
prisoners’ dilemma game shows how individuals acting independently may
be faced with a social dilemma.
Evidence suggests that individuals are not solely motivated by self-
interest. Altruism, peer punishment, and negotiated agreements all
contribute to the resolution of social dilemmas. There may be conflicts of
interest over the sharing of the mutual gains from agreement, or because
individuals prefer different equilibria, but social preferences and norms
such as fairness can facilitate agreement.
Concepts introduced in Unit 4
Before you move on, review these definitions:
• Game
• Best response
• Dominant strategy equilibrium
• Social dilemma
• Altruism
• Reciprocity
• Inequality aversion
• Nash equilibrium
• Public good
• Prisoners’ dilemma
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4.15 REFERENCES