Question

4. Consider the following game that is played T times. First, 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 again, and so on. The payoff for the whole game is the sum of the payoffs a player obtains in the T plays of the game A 3,1 4,0 0,1 В 1,5 2,2 0,1 C 1,1 0,2 1,2 (a) (10%) Suppose T-2. Is the following outcome path one that can be obtained from subgame perfect Nash equilibrium strategies? (If so, write down the strategies, if not explain why not (B,d) in the first round, (A,d) in the second round (b) (7%) Suppose T-3 and you are checking whether it is possible for subgame-perfect equilibrium strategies to support an outcome of (B,e) in the first round. Describe briefly in words the process you will follow to check this. Begin with: "A stage-game Nash equilibrium (I am confining myself to pure strategies) must be played in the last round, but players can co-ordinate on which one to play based on past outcomes. Therefore, I can sustain the following outcomes in the second-last round (c) (8%) Is it possible to sustain (as part of a SPNE) (Bo) as an outcome in the first round of a T-3 game? Write down the strategies that will do it, if the answer is "yes" and explain why not if the answer is "no". (Hint: (B,e) is not a Nash equilibrium if the game is played only once-both the row player and the column player have incentives to deviate So in order for each individual not to deviate, each must be rewarded sufficiently in what follows if he or she does not deviate and get worse payoffs if they do. Use your answer to (a) above.)

Answer 1