Consider the following game between One (who chooses rows) and Two (who chooses

Question

Consider the following game between One (who chooses rows) and Two (who chooses columns) L M | 4.0 | 0.1 | -1.-100 ID 1,1 0,3 a. Find the Nash equilibria of the one-shot game. Now imagine that the game is repeated infinitely often, with discount factor ? near to l. b. Construct a pure strategy Nash equilibrium with a different (from the ones found in a.) average payoff. C. characterize the set of possible subgame perfect equilibrium payoff in the limit when ? 1 (No construction or proof are required here.)

Explanation / Answer

a.There is one Nash equilibrium in pure strategies in this game and this is given by (D,R) with payoffs of (0,3). This is where each player does the best he can given what the other player does.

b. With the infinitely repeated game the long run outcome will be that the players will cooperate and with the discount factor near to 1 and so the long run equilibrium will be (D,L) with payoffs of (2,2). This is the long run equilibrium.

c. The subgame perfect equilibrium will be where there will be a Nash equilibrium in every subgame of the stage game.Thus in this case the subgame perfect Nash equilibrum will be playing (D,L) in every stage. Thus there will be cooperation in every stage of the repeated game.

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