Using Contracts to Influence the Outcome of a Game

We consider how much influence a center can exert on a game if its only power is to propose contracts to the agents before the original game, and enforce the contracts after the game if all agents sign it. Modelling the situation as an extensiveform game, we note that the outcomes that are enforceable are precisely those in which the payoff to each agent is higher than its payoff in at least one of the Nash equilibria of the original game. We then show that these outcomes can still be achieved without any effort actually expended by the center: We propose a mechanism in which the center does not monitor the game, and the contracts are written so that in equilibrium all agents sign and obey the contract, with no need for center intervention.