Pure-strategy equilibrium in Bayesian potential games with absolutely continuous information

We prove the existence of a pure-strategy Bayesian Nash equilibrium in Bayesian games with absolutely continuous information and a Bayesian potential that is upper semi -continuous in actions for any realization of the players' types. In particular, all Bayesian potential games with finitely many actions and absolutely continuous information possess a pure-strategy Bayesian Nash equilibrium. (c) 2023 Elsevier Inc. All rights reserved.