The paper shows that Perfect Bayesian equilibria need not be unique in the strategic communication game of Crawford and Sobel (1982). First, different equilibrium partitions of the state space can have equal cardinality, despite fixed prior beliefs. Hence, there can be different equilibrium...

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. We fully characterize the distributions over actions, states, and signals that obtain in any (sequential) communication...