Information Transmission in Revision Games

Revision games model a situation in which players can prepare their actions during a pre-play phase. We introduce one-sided incomplete information in two coordination games, one of common interest and one of opposing interest, and study how the pre-play phase affects coordination. We find that in the common interest game, the unique Bayesian equilibrium is such that the informed player will signal the state of the world through her prepared action, unless the pre-play phase is about to finish, in which case she seeks to coordinate with the other player. In the opposing interest game, the equilibrium is similar when the informed player is the one receiving less opportunity to revise her actions. When it is the uninformed player who receives less revision opportunities, we show that it is possible no information is revealed if both players are initially coordinated, but some information must be revealed if they are initially miscoordinated.