Pre-play promises, threats and commitments under partial credibility

The paper examines how pre-play communication between players with partial credibility affects the ensuing strategic interaction. We consider an environment where players are uncertain about the economic and psychological costs of reneging on promises but learn these at the time of their implementation. We demonstrate that in the equilibrium both players make promises. The latter are partially effective in terms of achieving collusive outcomes and improving the players' payoffs under strategic complementarity, where promises are used to signal future collusive behavior. In contrast, under strategic substitutability the ability to make a promise can be used to signal future aggressive behavior and one of the players may even get a lower expected (before the type is revealed) payoff than in the game without communication.