Bayesian Markov Games with Explicit Finite-Level Types

We present a new game-theoretic framework where Bayesian players engage in a Markov game and each has private but imperfect information regarding other players' types. Instead of utilizing Harsanyi's abstract types and a common prior distribution, we construct player types whose structure is explicit and induces a finite level belief hierarchy. We characterize equilibria in this game and formalize the computation of finding such equilibria as a constraint satisfaction problem. The effectiveness of the new framework is demonstrated on two ad hoc team work domains.