Finite Depth of Reasoning and Equilibrium Play in Games with Incomplete Information

The standard framework for analyzing games with incomplete information models players as if they have an infinite depth of reasoning. This paper generalizes the type spaces of Harsanyi (1967–1968) so that players can have a finite depth of reasoning. We do this by restricting the set of events that a player of a finite depth can reason about. This allows us to extend the Bayesian-Nash equilibrium concept to environments with players with a finite depth of reasoning. We demonstrate that the standard approach of modeling beliefs with Harsanyi type spaces fails to capture the equilibrium behavior of players with a finite depth, at least in certain games. Consequently, the standard approach cannot be used to describe the equilibrium behavior of players with a finite depth in general. The same result can be shown to hold for rationalizability, showing that the results do not hinge on the specifics of the solution concept.