3. Consider a repeated version of the following stage game: Player 2 Y 10, 10 В 20, —20 A -20, 20 0,4 Player 1 6, 6 2,4 C 4,0 4,2 3,3 Specifically, the stage game is played twice. For simplicity, assume that players do not discount future payoffs, or in other words, & = 1. (a) Identify all Nash equilibria, pure or mixed, of the stage game. Hint: begin with IESDS on the stage game. Which of these equilibria gives the highest payoff to each player? Which gives the lowest? (b) Verify that there is not an SPNE in which (A, X) is played in the first stage. (Hint: the equi- libria with the highest and lowest payoffs from part (a) serve as the best possible reward and punishment.)
3. Consider a repeated version of the following stage game: Player 2 Y 10, 10 В 20, —20 A -20, 20 0,4 Player 1 6, 6 2,4 C 4,0 4,2 3,3 Specifically, the stage game is played twice. For simplicity, assume that players do not discount future payoffs, or in other words, & = 1. (a) Identify all Nash equilibria, pure or mixed, of the stage game. Hint: begin with IESDS on the stage game. Which of these equilibria gives the highest payoff to each player? Which gives the lowest? (b) Verify that there is not an SPNE in which (A, X) is played in the first stage. (Hint: the equi- libria with the highest and lowest payoffs from part (a) serve as the best possible reward and punishment.)
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.9P
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