Believing when credible: talking about future intentions and past actions

In an equilibrium framework, we explore how players communicate in games with multiple Nash equilibria when messages that make sense are not ignored. Communication is about strategies and not about private information. It begins with the choice of a language, followed by a message that is allowed to be vague. We focus on equilibria where the sender is believed whenever possible, and develop a theory of credible communication. We show that credible communication is sensitive to changes in the timing of communication. Sufficient conditions for communication leading to efficient play are provided.