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Paper Code No: ECON
Examiner: Nicolas de Roos School: ULMS Department: Economics
e-mail: [email protected]
ACADEMIC YEAR 2024-
MOCK MID-TERM
ECON322 GAME THEORY
Instructions:
- Read the questions and any additional instructions carefully.
- You should attempt ALL the questions.
- Each question is worth 25 marks.
- You must provide explanations to your answers to obtain full marks.
- The total number of marks available is 100.
- This assessment is open-book.
- Submission Deadline: Wednesday 30/10/2024, at 2pm (subject to support plans)
- Al and Bo play a public contribution game. Each starts with $9. Each can choose to con- tribute either $9 or $0 to a common pot. If at least one player contributes, the pot returns $ to both players with probability n/2, where n is the number of contributors.
(a) Suppose that Al and Bo both have preferences over monetary amounts x that are repre- sented by the utility function u(x) = x. i. Write out the game in matrix form. [6 marks] ii. Do either of the players have any dominant strategies? [3 marks] iii. Identify any Nash equilibria to the game. [3 marks] (b) Suppose that Al and Bo both have preferences over monetary amounts x that are repre- sented by the utility function u(x) =
x. i. Write out the game in matrix form. [7 marks] ii. Do either of the players have any dominant strategies? [3 marks] iii. Identify any Nash equilibria to the game. [3 marks]
- Consider the following game, where x, y ∈ R:
Rohan
Colin d e f g h a 3 , 2 1 , 2 2 , 3 3 , y 2 , 1 b 3 , 2 4 , 3 2 , 4 4 , 3 2 , 3 c 3 , 2 0 , 1 x, 2 4 , 1 1 , 0
(a) Do there exist values of y such that Colin has a weakly dominant strategy? [5 marks] (b) Do there exist values of x such that Rohan has a strictly dominant strategy? [5 marks] (c) Let x = 5 and y = 3. Solve the game for the Iterated Elimination of Strictly Dominated Strategies. [5 marks] (d) Let x = 5 and y = 3. Solve the game for the smallest set of strategies that survive the Iterated Elimination of Weakly Dominated Strategies. [Note: to obtain the smallest set of IEWDS, delete any weakly dominated strategies as early as possible.] [5 marks] (e) Let x = 2 and y = 2. Identify any Nash equilibria. [5 marks]
