ECON 20005: Competition and Strategy
Assignment One
Semester 2, 2024
Administrative Rules
• Due date: 11:59 PM on 18 August, 2024. There is a 3-hour grace period for late sub-
missions, so you can submit your assignment without penalty before 3:00 AM on the next
day.
• Submission: Submit your solution as one pdf file via Gradescope following the instructions
provided on the website.
• Weight: The assignment is worth up to 10% of your final mark. You need to show all your
work to get partial or full credit.
• Late Submission: The assignment may be submitted late up to 2 days after the deadline
with a 15% penalty per day.
• Collaboration: Students are allowed to work together, but each must submit their own
unique final copy of the assignment.
• Plagiarism: Plagiarism will be taken very seriously. See http://academichonesty.unimelb.edu.au.
• Terminology:
– Throughout: “NE” refers to Nash Equilibrium/Equilibria; “SPNE” refers to Subgame
Perfect Nash Equilibrium/Equilibria; “PSNE” refers to Pure-strategy Nash Equilib-
rium/Equilibria.
– Throughout: “Briefly explain” means explain in no more than 3 sentences.
Question 1: Intel and AMD
Intel and AMD (Advanced Micro Devices) compete strategically in the market for CPUs (central
processing units) for both consumer and enterprise computers. Intel has been a dominant player
in the market while AMD struggled for many years to compete with Intel.
In response to its market position, AMD can choose either “No Investment (NI)”, “Modest
Investment (MI)”, or “Heavy Investment (HI)” in new technology and R&D. If NI, AMD’s and
Intel’s revenues are $1000 and $2000, respectively. If AMD chooses to invest, MI costs $100,
and HI costs $200. After seeing AMD’s investment, Intel subsequently chooses whether to run
a marketing campaign, choosing either “Market” (M) or “Not Market” (NM). The cost of the
marketing campaign to Intel is C.
AMD’s investment yields “Success” (S) or “No Success” (NS) with probabilities of p and 1−p.
If AMD invests MI then p = 0.4; if AMD invests HI then p = 0.8. If Intel does market, then
AMD’s and Intel’s revenues are $1600 and $2000 respectively if AMD’s investment is successful,
and $800 and $2200 respectively if AMD’s investment is not successful. If Intel does not market,
then AMD’s and Intel’s revenues are $1600 and $1500 if AMD’s investment is successful, and
$1000 and $2000 if AMD’s investment is not successful. The outcome of AMD’s investment is
determined by Nature after AMD and Intel makes their choices.
1.1 What is AMD’s payoff/profit if it chooses to invest heavily, Intel does not market, and the
investment is successful? What is Intel’s payoff (as a function of C) if it chooses to market
and AMD’s investment is not successful?
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1.2 Determine whether information is perfect or imperfect in this game. Briefly explain.
1.3 Present this game using a game tree (i.e., in extensive form). Please write Intel’s payoff as
a function of C.
1.4 List all the possible strategies of the sequential game for AMD and Intel.
1.5 Suppose C = $400, What are the SPNE strategies for each player? What are the SPNE
path and payoffs?
1.6 What is the maximum value of C such that Intel would always invest in marketing in a
SPNE? (If M or NM yields the same payoff, then Intel will choose M .)
1.7 Suppose C = $400, represent this game in normal form.
1.8 Find the PSNE using the normal form (from 1.8) and compare it with the SPNE that you
found. Briefly explain why there is a difference.
2+1+4+3+4+2+4+3=23 Marks
Question 2: Harry Potter and Ron Weasley’s Magical Adventure
Harry and Ron, two friends who respectively live at 4 Privet Drive and The Burrow, are considering
taking a last-minute adventure together on Harry’s birthday. They consider using Floo Powder
to travel to either Godric’s Hollow (GH) or the Quidditch World Cup Final (Q). Unfortunately,
Harry’s uncle, Vernon Dursley, forbids Harry from contacting his friends at Hogwarts, so there is
no direct communication with Ron. That means they must decide where to go simultaneously.
Another complication is that Harry loves visiting Godric’s Hollow, his birthplace, while Ron
loves supporting his favorite Quidditch team at the World Cup Final. If Harry and Ron go to
Godric’s Hollow together, they respectively get happiness of 8 and 1. In contrast, if they go to
the Quidditch World Cup together, they respectively get happiness of 3 and 5. If they end up in
different places, they will both be miserable and receive happiness of -1 regardless of where each
ends up.
2.1 Draw the normal and extensive form of the game. (The row player is Harry in the normal
form game.)
2.2 Find all PSNE.
2.3 If there are multiple equilibria, which equilibrium do you think Harry and Ron are more
likely to choose? Briefly explain.
2.4 Now suppose all payoffs remain the same, except that Harry makes his choice of destination
first, and then Ron chooses where to go upon seeing Harry’s choice. Draw the extensive
form of this new game.
2.5 Characterize the SPNE (i.e., state the SPNE path, each player’s SPNE strategies, and the
SPNE payoffs).
2.6 Does this game have a first or second mover advantage? Briefly explain.
2.7 Keeping with the same sequential game from 2.4, now suppose that before Harry or Ron
make their destination choices, Ron has the option to first purchase a special Quidditch pack
for a cost of 5. If he buys the Quidditch pack, Ron will receive a Omnioculars at the World
Cup, giving Ron a happiness of 15. Assume all other payoffs remain the same as before from
part 2.4 (for example, if Ron buys the Quidditch pack and ends up in the World Cup alone,
his net payoff is 15-5-1=9). Draw the extensive form of this game and characterize its SPNE
(i.e., state the SPNE path, each player’s SPNE strategies, and the SPNE payoffs).
2
2.8 Can the Quidditch pack be seen as a sort of “commitment device” for Ron to ensure they
end up at the Quidditch World Cup? Briefly explain.
5+2+1+2+3+3+4+2=22 Marks
Question 3: Backward Induction
Cameron and Andy are playing a game called “Race to 10”. Cameron goes first, and the players
take turns choosing either 1, 2, or 3. In each turn, they add the new number to a running total.
The player who brings the total to exactly 10 wins the game.
3.1 Suppose Cameron can take the number to 6, and it is Andy’s turn. Briefly explain how
Cameron can react to Andy’s possible actions to guarantee himself victory.
3.2 Suppose Cameron can take the number to 2. What strategy should Cameron use to guarantee
himself victory? (Hint: Use your answer from 3.1 to roll back.) Briefly explain.
3.3 Now start from the beginning of the game. If both Cameron and Andy play optimally,
who will win the game? Does the game have a first-mover advantage or a second-mover
advantage?
3.4 What if the game is “Race to 12”? Does the result change?
1+1+1+2=5 Marks