Two-speed evolution with pre-play communication and limited flexibility

This paper studies the effects of pre-play communication on equilibrium selection in 2×22×2 symmetric coordination games. The players repeatedly play a coordination game preceded by an opportunity to exchange payoff irrelevant messages and gradually adjust their behavior. In short run, the players' access to the actions of the coordination game may be restricted. While the players can revise the set of accessible actions only occasionally, they frequently adjust their behavior in the cheap-talk game, taking the set of currently available actions as given. We obtain an efficient-equilibrium-selection result if the underlying coordination game satisfies the self-signaling condition. On the other hand, if the game is not self-signaling, both the efficient and the inefficient equilibrium outcomes are stable.