Lipschitz recursive equilibrium with a minimal state space and heterogeneous agents

Abstract

This paper analyzes the Lucas tree model with heterogeneous agents and one asset. We show the existence of a minimal state space Lipschitz continuous recursive equilibrium using Montrucchio (1987) results. The recursive equilibrium implements a sequential equilibrium through an explicit functional equation derived from the Bellman Equation. Our method also allows to prove existence of a recursive equilibrium in a general class of deterministic or stochastic models with several assets provided there exists a Lipschitz selection on the demand correspondence. We provide examples showing applicability of our results.