Abstract
We add a round of pre-play communication to a finite two-player game played by a population of players. Pre-play communication is cheap talk in the sense that it does not directly enter the payoffs. The paper characterizes the set of strategies that are stable with respect to a stochastic dynamic adaptive process. Periodically players have an opportunity to change their strategy with a strategy that is more successful against the current population. Any strategy that weakly improves upon the current poorest performer in the population enters with positive probability. When there is no conflict of interest between the players, only the efficient outcome is stable with respect to these dynamics. For general games the set of stable payoffs is typically large. Every efficient payoff recurs infinitely often.
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