The paper analyzes the role of the structure of communication - i.e. who is talking with whom - on the choice of messages, on their credibility and on actual play. We run an experiment in a three-player coordination game with Pareto ranked equilibria, where a pair of agents has a profitable joint deviation from the Pareto-dominant equilibrium. According to our analysis of credibility, the subjects should communicate and play the Pareto optimal equilibrium only when communication is public. When pair of agents exchange messages privately, the players should play the Pareto dominated equilibrium and disregard communication. The experimental data conform to our predictions: the agents reach the Pareto-dominant equilibrium only when announcing to play it is credible. When private communication is allowed, lying is prevalent, and players converge to the Pareto-dominated equilibrium. Nevertheless, at the individual level, players’ beliefs and choices tend to react to messages even when these are non-credible.