ECOS3012 Strategic Behaviour
Quiz 1 solution
1. Watch the following clip from "A Beautiful Mind":
https://www.youtube.com/watch?v=LJS7Igvk6ZM
Let’s consider the scenario in this clip: each guy strictly prefers to dance with the blonde
than her brunette friends, and each guy strictly prefers to dance with some girl than being
alone. Also, assume that a girl will refuse to dance with anyone if she is simultaneously
approached by two or more guys, but will agree to dance if she is approached by only one
guy.
In the movie, "John Nash" proposes that they should each approach a brunette girl and leave
the blonde alone.
Does this proposed strategy profile constitute a Nash equilibrium?
Answer: This is not a Nash equilibrium because there is a unilateral profitable deviation:
"If all the other guys are approaching some brunette, it’s not optimal for me to follow
the same strategy because, in this case, I am better-off approaching the blonde."
2. (Continue) Does "John Nash"’s proposed strategy profile maximise the total social welfare
of his group of guys?
Answer: His proposition does not maximise their total welfare. Their welfare can be im-
proved if one of them dances with the blonde rather than a brunette.
3. Two female funnel web spiders are contesting a desirable nesting site. Each can either be-
have aggressively (Hawk) or submissively (Dove). Both behaving aggressively leads to a
disastrous fight, but it is better to be a Hawk if the other is a Dove.
Spider 2
Hawk Dove
Spider 1
Hawk 0, 0 3, 1
Dove 1, 3 2, 2
Select all strategy pairs that survive the iterative elimination of strictly dominated strategies.
Answer: All pairs work. Hawk is the best response when the opponent chooses Dove, and
Dove is the best response when the opponent chooses Hawk. Therefore, no strategy is
strictly dominated.
4. (Continue) Select all pure-strategy Nash equilibrium.
Answer: (Hawk, Dove) and (Dove, Hawk).
When both spiders choose Hawk, one of them will want to switch to Dove.
When both choose Dove, one of them will want to switch to Hawk.
When one chooses Dove and one chooses Hawk, neither wishes to deviate.
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5. Alicia, Kate, and Lauren are ecstatic. They’ve just landed tickets to attend this week’s seg-
ment of The Voice. The three teens have the same favorite among the four contestants that
remain: Amy. They’re determined to take this opportunity to make a statement. They come
up with a plan to wear T-shirts that spell out “AMY” in large letters. Lauren is to wear a
T-shirt with an “A,” Kate with an “M,” and Alicia with a “Y.” If they pull this stunt off,
who knows—they might end up on national television! While they all like this idea, each
is tempted to wear instead an attractive new dress just purchased from their latest shopping
expedition. It’s now an hour before they have to leave to meet at the studio, and each is at
home trying to decide between the dress and the lettered T-shirt. What will they wear in the
end? Find all pure-strategy Nash equilibria of this game.
Alicia chooses Y Alicia chooses dress
Kate Kate
M dress M dress
Lauren A 2, 2, 2 0, 1, 0 Lauren A 0, 0, 1 0, 1, 1dress 1, 0, 0 1, 1, 0 dress 1, 0, 1 1, 1, 1
Answer: (A, M, Y) and (dress, dress, dress).
Note: to select best responses, Lauren compares her payoffs within each column of each
matrix; Kate compares her payoffs within each row of each matrix; Alicia compares her
payoffs from the same cell in each of the two matrices.
6. Aragorn and Frodo have a common goal: they want to destroy the Dark Lord Sauron.
Aragorn must decide whether he will declare war again Sauron at the Black Gate to distract
Sauron’s attention. Frodo must decide whether he will climb up Mount Doom to destroy the
One Ring that contains Sauron’s magical power.
If Aragorn chooses to war and Frodo chooses to climb up Mount Doom, they will have a
happy ending: while Sauron is distracted by the war, Frodo safely arrives at Mount Doom
and destroys the ring. Since Sauron’s power disappears once the ring is destroyed, Aragorn
wins the war.
If Frodo chooses not to climb up Mount Doom, he will be safe but Aragorn will die at the
war; if Aragorn chooses not to declare war, he will be safe but Frodo will be killed on his
way to Mount Doom. Both Frodo and Aragorn prefer life over death, and they prefer to live
in a peaceful world without Sauron.
Question: This scenario is the most similar to which of the following games?
A. Prisoners’ dilemma
B. Penalty kick
C. Hawk dove
D. Battle of the sexes
E. Stag hunt
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Answer: E
7. Jim and Buzz are two bored, young people. Not knowing what to do with their lives, they
decide to play "the chicken game":
In this game, they drive towards each other on a collision course. The first one swerving is
the chicken, and the one keeping his way will be the winner. If they both swerve they are
both chickens, but the stigma will not be as high as in the case on is the only coward. The
worst-case scenario occurs if they both keep going and crash into each other. They would
have been very brave but also lost their lives. The following table summarises this game.
Buzz
Swerve Keep going
Jim
Swerve 2, 2 1, 10
Keep going 10, 1 -999, -999
Find all pure-strategy Nash equilibrium of this game.
Answer: (Swerve, Keep going) and (Keep going, Swerve). Best responses of the players
are highlighted in bold.
8. (Continue)
The chicken game is essentially identical to which of the following games?
A. Prisoners’ dilemma
B. Penalty kick
C. Hawk dove
D. Battle of the sexes
E. Stag hunt
F. None.
Answer: It is equivalent to the Hawk-Dove game. Swerve = Dove. Keep going = Hawk.
Even though the exact payoff numbers are different, the players’ preference ranking
over the possible outcomes are the same.