Preopening and Equilibrium Selection

Abstract

We introduce a form of pre-play communication that we call for standard normal form, two player games. During the preopening players announce their strategy using a communication system which is subject to stochastic failures. Players payoffs depend on the action profile posted on the system at the end of the preopening. We show that the preopening allows players to coordinate on one pure strategy equilibrium of the game when the system failures hit the two players idiosyncratically. In such a case the preopening always leads the players to select the Pareto superior Nash equilibrium when this exhibits the maximum attainable payoff for each player. Moreover, in the class of two action games of conflicting interests the preopening leads to select the equilibrium preferred by the player with (i) the strongest preference over different equilibria, (ii) the lower cost of miscoordination or (iii) the less efficient posting system.