Consider an infinitely repeated game with the following stage game:
Suppose that this repeated game is the underlying game in a contractual setting with external enforcement. Specifically, an external enforcer will compel transfer a from player 2 to player 1 in every period in which (N, I) is played, transfer b from player 2 to player 1 in every period in which (I, N) is played, and transfer g from player 2 to player 1 in every period in which (N, N) is played. The numbers a, b, and g are chosen by the players in their contract before the repeated interaction begins. These numbers are fixed for the entire repeated game. Assume that the players discount the future using discount factor δ
(a) Suppose there is full verifiability, so that , ß, and g can be different numbers. Under what conditions on δ is there a contract such that the players choose (I, I) in each period in equilibrium?
(b) Suppose there is limited verifiability, so that α = ß = before the repeated game is played, they can also make an up-front monetary transfer m from player 2 to player 1. Assume that if the players do not reach an agreement on α, ß, g, and m, then they will not play the repeated game and each player will get 0. If player 1's bargaining weight is π1 = 2/3 what does the standard bargaining solution predict will be the value of m?