Consider an infinite-period repeated prisoners' dilemma game in which a long-run player 1 faces a sequence of short-run opponents. (You dealt with games like this in Exercise 8 of Chapter 22.) Formally, there is an infinite number of players-denoted
who play as player 2 in the stage game. In period t, player 1 plays the following prisoners' dilemma with player 2t .
Assume that all of the players observe the history of play. Let d denote the discount factor of player 1. (a) Show that the only subgame perfect equilibrium involves play of (D, D) each period.
(b) Next suppose that the players 2t have the opportunity to buy and sell the right to play the game each period. Formally, suppose that in order for player 2t to play the stage game in period t, this player must purchase the right from player 2t-1 . Model the negotiation between successive players 2t-1 and 2t as a joint decision. Further, assume the outcome of negotiation is consistent with the standard bargaining solution. Under what conditions on bargaining weights and the discount factor can (C, C) be supported over time?