Stationary Markov Equilibria

Abstract

Conditions are established under which there are equilibria (in various settings) described by ergodic Markov processes with a Borel state space S. Let [Rho](S) denote the probability measures on S, and let s [approaching] G(s) [is a subset of] [Rho](S) be a (possibly empty-valued) correspondence with closed graph. A non-empty measurable set J [is a subset of] S is self-justified if G(s) [intersects] [Rho](J) is not empty for all s [an element of] J. A Time-Homogeneous Markov Equilibrium (THME) for G is a self-justified set J and a measurable selection II: J [approaching] [Rho] (J) from the restriction of G to J. The paper gives sufficient conditions for existence of compact self-justified sets, and applies the theorem: If G is convex-valued and has a compact self-justified set, then G has an THME with an ergodic measure. Coauthors are J. Geanakoplos, A. Mas-Colell, and A. McLennan. Copyright 1994 by The Econometric Society.