Trading favors: optimal exchange and forgiveness.

This paper characterizes optimal renegotiation proof public perfect equilibrium in a repeated partnership game. The model was originally introduced by Mobius. Players have random arrival of endowments which are privately observed that are more valued by the partner than the player receiving the endowment. Optimal cooperation requires agents to give the endowments received to the partners. An algorithm is provided to find the best public perfect equilibrium. In this equiibrium, the relative price of current for future favors (endowment transfers) varies sistematically with the history of favors received. Forgivness is also a property of the equilibrium: after periods of no favors from both parties, utilities tend to converge