Bayesian Approach with Finite Hierarchies of Beliefs: Bounded Rationality in Strategic Form Games

We present a Bayesian framework based on the finite hierarchies of beliefs to study the decision problems in strategic form games. The model allows us to analyze the behavior of bounded rational players as well as that of fully rational players. We define the degree of ``boundedness'' by the complexity of thought process (number of consistent layers of beliefs) and the ``fully rational'' player is simply a player of complexity-$\infty$ whose thought process continues ad infinitum. We show conditions under which the set of ``Bayesian strategies of complexity-$k$'', strategies taken by the Bayesian player of complexity-$k$, coincides with the set of ``$k$th order iteratively undominated strategies''. The conditions are studied for iterative elimination of strictly and weakly dominated strategies. The results are applied to analyze the well known paradoxes in games studied by Rubinstein (1989) and Reny (1992).