Consider the prisoner's dilemma with payoffs as given below: C D C 1,1 1+g,-l D -l,...

 

Transcribed Image Text:

Consider the prisoner's dilemma with payoffs as given below: C D C 1,1 1+g,-l D -l, 1+g 0,0 g>0,l> 0 Suppose that the game is repeated twice, with the following twist. If a player chooses an action in period 2 which differs from her chosen action in period 1, then she incurs a cost of e. Players maximize the sum of payoffs over the two periods, with discount factor d = 1. (a) Suppose that g <1 and 0 < g < < l. Suppose each player plays the strategy which chooses C at t = 1, and chooses C at t = 2 if (C,C) has been played at t = 1, and D otherwise. Show that this is a subgame perfect equilibrium. (b) Let > 0 be arbitrary. Show that there is always a subgame perfect equilibrium where (D, D) is played in both periods. Consider the prisoner's dilemma with payoffs as given below: C D C 1,1 1+g,-l D -l, 1+g 0,0 g>0,l> 0 Suppose that the game is repeated twice, with the following twist. If a player chooses an action in period 2 which differs from her chosen action in period 1, then she incurs a cost of e. Players maximize the sum of payoffs over the two periods, with discount factor d = 1. (a) Suppose that g <1 and 0 < g < < l. Suppose each player plays the strategy which chooses C at t = 1, and chooses C at t = 2 if (C,C) has been played at t = 1, and D otherwise. Show that this is a subgame perfect equilibrium. (b) Let > 0 be arbitrary. Show that there is always a subgame perfect equilibrium where (D, D) is played in both periods.

Answer rating: 100% (QA)

a Suppose that g 1 and 0 g This strategy is a subgame perfect equilibrium SPE because it is a Nash e... View the full answer