Coordination and the Potential for Self-Sacrifice

An extension of games is proposed, where players are given the option of incurring costs. This extension allows players to signal their intended strategy in the original game. We apply the logic of forwards and backwards induction, without additional equilibrium assumptions, by using iterated deletion of weakly dominated strategies as a solution concept. For a class of games, this is sufficient to select a unique outcome in the extended game, even when the original game has multiple equilibria. In these games, the option of incurring a cost enables a player to credibly indicate that he will play the strategy which leads to his best outcome. Furthermore, the player does not have to incur any costs to achieve this - the option alone suffices. In particular, when all the players’ objectives coincide, they can coordinate and costlessly achieve their mutually preferred outcome. The relationship with signaling games, where players signal (exogenously determined private information, is also discussed.