Answer to Question #229033 in Microeconomics for Nick

Question

Consider the following normal form game:

1/2 ----L-----------R

U----(1,1)-------(-2,6)

D----(6,-2)------(-1,-1)

What difference does it make if the game is played only once or is repeated an infinite number of times? Show that, with infinite repetitions, an average payoff pair (2, 2) can be obtained if the players alternate between two different strategy pairs. Show that the average payoffs (2, 2) are also enforceable if the players follow a simple trigger strategy.

Answer 1

If the game is played once there are two nash equilibria that is (U,L) and (D,R) that is (1,1) and (-1,-1) which is different from the repeated strategies.

If the game is played an infinite number of times two strategies will always be chosen that is

(U,R) and (D,L) which gives an average payoff of (2,2).

If the players follow a simple trigger strategy, they will always choose two strategies that also gives maximum payoffs that is (U,R) and (D,L) which results in an average payoff of (2,2).