Question Nine (worth eight pointsPart (a) is worth two points and Part (b) is worth six points)

(a) Assume that Al and Alecia have to decide whether to play a black card or a red card. If Al plays the red card he receives $100 and Alecia receives nothing. If Alecia plays the red card she receives $100 and Al receives nothing. If Al plays the black card he receives $0 and Alecia receives $300. If Alecia plays the black card she receives $0 and Al receives $300. Set up the matrix and prove that equilibrium occurs with both playing the red card.

(b) Economists want to find ways to encourage people to cooperate. One possibility: have people engage in repeated interactions. Use the information in part (a) to answer this part of the question. Assume that Al and Alecia are going to play the game 10 times. Explain why, in the last round it would make sense to play red and then explain why, if that makes sense, that Al and Alecia should play the red card in all rounds.

Explain in great detail