Language and coordination games

Abstract

Intuitively, if players can communicate, they should be able to reach coordinated play in a coordination game. However, simply adding a communication stage before the play of the game does not render coordination as a unique prediction. To further refine the set of equilibria, Farrell suggested that a self-committing cheap talk statement about one’s planned behavior should be believed and thus would for sure lead to coordinated play. Aumann, however, argued that the statement has to be both self-committing and self-signaling for it to guarantee coordination. In this paper, the concept of common knowledge of language is formally incorporated into the cheap talk extension game. This paper shows that, if the stage game satisfies both the self-committing and the self-signaling condition, then every iteratively admissible outcome in the language game constitutes a coordinated play and gives the Sender her Stackelberg outcome. On the other hand, this paper identifies a class of generic games that violate self-signaling condition where every strategy profile of the stage game is an iteratively admissible outcome of the language game. This result supports Aumann’s argument that the self-signaling condition is necessary for coordinated play to be guaranteed by one-sided communication.