Non-Uniqueness of Equilibria in One-Shot Games of Strategic Communication

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 action profiles with the same size. Second, provided a Perfect Bayesian equilibrium exists, different message rules and beliefs can hold in other equilibria inducing the same action profile.