Incomplete Information and Equilibrium
In games with incomplete information Bayesian equilibrium constitutes the prevailing solution concept. We show that Bayesian equilibrium generalizes correlated equilibrium from complete to incomplete information. In particular, we provide an epistemic characterization of Bayesian equilibrium as well as of correlated equilibrium in terms of common belief in rationality and a common prior. Bayesian equilibrium is thus not the incomplete information counterpart of Nash equilibrium. To fill the resulting gap, we introduce the solution concept of generalized Nash equilibrium as the incomplete information analogue to Nash equilibrium, and show that it is more restrictive than Bayesian equilibrium.
Joint work with Christian Bach