STATIONARY MARKOV EQUILIBRIA

We establish conditions which (in various settings) guarantee the exis tence of equilibria described by ergodic Markov processes with a Borel state space S. Let P(S) denote the probability measures on S, and let s bar arrow pointing right G(s) subset-of P(S) be a (possibly empty-v alued) correspondence with closed graph characterizing intertemporal c onsistency, as prescribed by some particular model. A nonempty measura ble set J subset-of S is self-justified if G(s) and P(J) is not empty for all s is-an-element-of J. A time-homogeneous Markov equilibrium (T HME) for G is a self-justified set J and a measurable selection PI: J --> P(J) from the restriction of G to J. The paper gives sufficient co nditions 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. The applications are (i) s tochastic overlapping generations equilibria, (ii) an extension of the Lucas (1978) asset market equilibrium model to the case of heterogene ous agents, and (iii) equilibria for discounted stochastic games with uncountable state spaces.