Stationary Bayesian–Markov Equilibria in Bayesian Stochastic Games with Periodic Revelation

Abstract

I consider a class of dynamic Bayesian games in which types evolve stochastically according to a first-order Markov process on a continuous type space. Types are privately informed, but they become public together with actions when payoffs are obtained, resulting in a delayed information revelation. In this environment, I show that there exists a stationary Bayesian–Markov equilibrium in which a player’s strategy maps a tuple of the previous type and action profiles and the player’s current type to a mixed action. The existence can be extended to K-periodic revelation. I also offer a computational algorithm to find an equilibrium.

Keywords

• Bayesian game
• stochastic game
• existence
• stationary Markov equilibrium
• periodic revelation