Equilibrium in Misspecified

We provide an equilibrium framework for modeling the behavior of an agent who holds a simplified view of a dynamic optimization problem. The agent faces a Markov Decision Process, where a transition probability function determines the evolution of a state variable as a function of the previous state and the agent’s action. The agent is uncertain about the true transition function and has a prior over a set of possible transition functions; this set reflects the agent’s (possibly simplified) view of her environment and may not contain the true function. We define an equilibrium concept and provide conditions under which it characterizes steady-state behavior when the agent updates her beliefs using Bayes’ rule. Unlike the case for static environments, however, an equilibrium approach for the dynamic setting cannot be used to characterize those steady states where the agent perceives that learning is incomplete. Two key features of our approach is that it distinguishes between the agent’s simplified model and the true primitives and that the agent’s belief is determined endogenously in equilibrium. ∗We thank Vladimir Asriyan, Hector Chade, Xiaohong Chen, Emilio Espino, Drew Fudenberg, Bruce Hansen, Philippe Jehiel, Bart Lipman, Jack Porter, Philippe Rigollet, Tom Sargent, Philipp Strack, Iván Werning, and several seminar participants for helpful comments. Esponda: Olin Business School, Washington University in St. Louis, 1 Brookings Drive, Campus Box 1133, St. Louis, MO 63130, [email protected]; Pouzo: Department of Economics, UC Berkeley, 530-1 Evans Hall #3880, Berkeley, CA 94720, [email protected].