Consider a two-player simultaneous-move game, with two strategies for each player. Player 1's strategy set is {(A, B) and Player 2's strategy set is {C, D}. State whether the following statements are True or False. If C is the strictly-dominant strategy for Player 2, and B is a weakly dominant strategy for Player 1, there can be infinitely many mixed-strategy Nash Equilibria of this game. If A is the strictly dominant strategy for Player 1 and C is the strictly dominant strategy for Player 2, then the (A,C) outcome must be a Pareto-efficient outcome of the game
Consider a two-player simultaneous-move game, with two strategies for each player. Player 1's strategy set is {(A, B) and Player 2's strategy set is {C, D}. State whether the following statements are True or False. If C is the strictly-dominant strategy for Player 2, and B is a weakly dominant strategy for Player 1, there can be infinitely many mixed-strategy Nash Equilibria of this game. If A is the strictly dominant strategy for Player 1 and C is the strictly dominant strategy for Player 2, then the (A,C) outcome must be a Pareto-efficient outcome of the game
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.9P
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Transcribed Image Text:Consider a two-player simultaneous-move game, with two strategies for each player.
Player 1's strategy set is {A, B} and Player 2's strategy set is {C, D}.
State whether the following statements are True or False.
If C is the strictly-dominant strategy for Player 2, and B is a weakly dominant strategy
for Player 1, there can be infinitely many mixed-strategy Nash Equilibria of this game.
If A is the strictly dominant strategy for Player 1 and C is the strictly dominant strategy
for Player 2, then the (A,C) outcome must be a Pareto-efficient outcome of the game.
Suppose that B is the strictly dominant strategy for Player 1 and D is the strictly
dominant strategy for Player 2, and that both players are better off in the (A, C)
outcome compared to the Nash Equilibrium outcome. Then:
The (A,C) outcome can be achieved in at least one period of a finitely-repeated (with
known end, i.e. both players know when the game is going to end) version of this
game.
The (A,C) outcome can be achieved in at least one period of the infinitely-repeated
version of this game.
The strategy profile where Player 1 always plays B and Player 2 always plays D is a
subgame-perfect equilibrium of the infinitely repeated version of this game.
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