In impromptu or ad hoc settings, participating players are precluded from precoordination. Subsequently, each player's own model is private and includes some uncertainty about the others' types or behaviors. Harsanyi's formulation of a Bayesian game lays emphasis on this uncertainty while the players each play exactly one turn. We propose a new game-theoretic framework where Bayesian players engage in a Markov game and each has private but imperfect information regarding other players' types. Consequently, we construct player types whose structure is explicit and includes a finite level belief hierarchy instead of utilizing Harsanyi's abstract types and a common prior distribution. We formalize this new framework and demonstrate its effectiveness on two standard ad hoc teamwork domains involving two or more ad hoc players.