Efficiency in strategic form games: A little trust can go a long way

We study the incentives of noncooperative players to play a cooperative game. That is, we look for individually rational, redistributive, pre-game agreements enacted in order to coordinate towards efficient equilibrium play. Contrasting with standard Nash equilibrium analysis, we assume that players can commit to the agreements they negotiate and that utility is verify and transferable. We show that agreeing on a proportional-exponential redistribution rule is individually rational and implements the socially efficient outcome as Nash equilibrium. Moreover, we show that this class of redistributional contracts may be naturally obtained as the outcome of Nash bargaining.