Commitments, intentions, truth and Nash equilibria

Games with multiple Nash equilibria are believed to be easier to play if players can communicate. We present a simple model of communication in games and investigate the importance of when communication takes place. Sending a message before play captures talk about intentions, after play captures talk about past commitments. We focus on equilibria where messages are believed whenever possible. Applying our results to Aumann's Stag Hunt game we find that communication is useless if talk is about commitments, while the efficient outcome is selected if talk is about intentions. This confirms intuition and empirical findings in the literature.