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Abstract:
We consider multi-stage games, where at each stage, players receive private signals about past and current states, past actions and past signals, and choose actions. States are allowed to be endogenous to past actions. We fully characterise the distributions over actions, states, and signals that obtain in any (sequential) communication equilibrium of any expansion of multi-stage games, i.e., when players can receive additional signals. We show that this coincides with the distribution over actions, states and signals that obtain in equilibria of a mediated game where players obey recommendations that are functions of past actions, and current and past signals and states. We interpret our results as revelation principles. We apply our characterization to bilateral bargaining.