a b c A (3,2) (5,0) (1,1) B (2,5) (4,4) (1,2) C (1,1) (0,2) (2,3) Players move s

Question

      a      b     c

A (3,2) (5,0) (1,1)

B (2,5) (4,4) (1,2)

C (1,1) (0,2) (2,3)

Players move simultaneously and independently. Then each player is informed about the actions taken by the other player in the first play and, given this, they play it three times. The payoff is the sum of the payoffs in the three rounds. Is it possible for (B,b) to be played in the first period of a subgame perfect Nash equilibrium? If so, write down the complete strategies that make this subgame perfect.

Suppose the game is played 10 times, the payoff being given by the sum as usual. Can (B,b) be played in the first round as part of a SPNE? In the 7th round? Describe the strategies if your answer is yes.

Thank you for helping

Explanation / Answer

a b c A (3,2) (5,0) (1,1) B (2,5) (4,4) (1,2) C (1,1) (0,2) (2,3) Players move s

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