On Existence Of Berk-Nash Equilibria In Misspecified Markov Decision Processes With Infinite Spaces

We present theorems on the existence of Berk-Nash equilibria in misspecified Markov Decision Processes with infinite action and state spaces. We extend the results of Esponda-Pouzo (2021) for finite state and action spaces to compact action spaces and sigma-compact state spaces with possibly unbounded payoff functions. This extension allows, for the first time, consideration of continuous distributions with possibly unbounded support. We provide several examples that span various areas in economic theory: neo-classical producer theory, the optimal savings problem, and identification and inference in econometric theory. The proofs use a recent technique in nonstandard analysis, originated by the second author, to extend known theorems for finite mathematical systems to infinite systems. This technique has already generated new results in probability theory, statistical decision theory, and general equilibrium theory, and is potentially applicable to a wide range of problems.