Summary: A model is presented where players communicate prior to the play of a two-player, complete-information game. Each of two common hypothesis is examined: That communication yields Nash-equilibrium outcomes, and that, within the equilibrium framework, communication yields Pareto-efficient equilibria. The strong version of each of these hypotheses is rejected but weaker results are established. The main result is that, if we assume equilibrium and that players communicate for a long time, then in every equilibrium of every game, each player will get a payoff at least as great as that of his worst Pareto-efficient Nash equilibrium.