Problem 5: Limited Punishment Consider the game in table 3. The game is repeated infinitely. Both players discount payoff streams using the discount factor & = 0.9. Players both play limited punishment trigger strategies with a punishment phase of T periods. Determine the length of the punishment period that is required to support (4, 4) as the payoff in every stage of a

Problem 5: Limited Punishment Consider the game in table 3. The game is repeated infinitely. Both players discount payoff streams using the discount factor & = 0.9. Players both play limited punishment trigger strategies with a punishment phase of T periods. Determine the length of the punishment period that is required to support (4, 4) as the payoff in every stage of a

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

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A principal can choose to make the allocation of tasks broad (B) or narrrow (N). At the same time an agent can choose to work put in high effort (H) or low effort (L). The payoffs are 20 to the principal and 30 to the agent is the actions chosen are B and L. For all other combinations of actions the payoffs are 0 to both players. Which of the following statements are true? DA Nash equilibrium of the game is (B, H) A Nash equilibrium is (N, L) There is no Nash equilibrium in pure strategies in this game. A Nash equilibrium is (N, H) A Nash equilibrium is (B, L)
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Consider the game in Table 1 and answer the following questions. (1) Write down each player's best response functions and find all the Nash equilibria. (2) For each action of each player, determine whether it is strictly, weakly, or not domi- nated by any other actions. Justify your answer. (3) Find the set of rationalizable action profiles by iteratedly eliminate strictly dominated actions. Clearly show the steps. TABLE 1. A Strategic Game L CR 2,2 1,2 3,3 2,3 1,2 0,3 0,3 1,2 2,1 2,2 M B
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Consider two players, P1 and P2, each can choose A or B. The payoff matrix as a result of the players' choices are listed below: P1 O (P1, P2) (A, A) O (P1, P2) = (A,A) O (P1, P2) = (A, A) A Identify the pure-strategy Nash equilibrium (P1, P2). (P1, P2) = (A, A) B There are multiple pure-strategy Nash equilibria. O There is no pure-strategy Nash equilibrium. -25 35 A 25 -35 P2 35 -45 B -35 45
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Two athletes of equal ability are competing for a prize of $10,000. Each is deciding whether to take a dangerous performance enhancing drug. If one athlete takes the drug, and the other does not, the one who takes the drug wins the prize. If both or neither take the drug, they tie and split the prize. Taking the drug imposes health risks that are equivalent to a loss of X dollars. a) Draw a 2×2 payoff matrix describing the decisions the athletes face. b) For what X is taking the drug the Nash equilibrium? c) Does making the drug safer (that is, lowering X) make the athletes better or worse off? Explain.