Date Added: May 2010
This paper studies the evolution of peoples' models of how other people think - their theories of mind. First, this is formalized within the level-k model, which postulates a hierarchy of types, such that type k plays a k time's iterated best response to the uniform distribution. It is found that, under plausible conditions, lower types co-exist with higher types. The results are extended to a model of learning, in which type k plays a k times iterated best response the average of past play. The results are also extended to the cognitive hierarchy model, and to the introduction of a type that plays Nash equilibrium.