We establish conditions which (in various settings) guarantee the existence of equilibria described by ergodic Markov processes with a Borel state space S. Let 9(S) denote the probability measures on S, and let s-G(s) c 4?(S) be a (possibly empty-valued) correspondence with closed graph characterizing intertemporal consistency, as prescribed by some particular model. A nonempty measurable set J c S is self-justified if G(s) n 9?(J) is not empty for all s E J. A time-homogeneous Markov equilibrium (THME) for G is a self-justified set J and a measurable selection TI: J-9 _(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. The applications are (i) stochastic overlapping generations equilibria, (ii) an extension of the Lucas (1978) asset market equilibrium mnodel to the case of heterogeneous agents, and (iii) equilibria for discounted stochastic games with uncountable state spaces.

“Naïve” Condorcet Jury Theorems automatically have “sophisticated” versions as corollaries. A Condorcet Jury Theorem is a result, pertaining to an election in which the agents have common preferences but diverse information, asserting that the outcome is better, on average, than the one that would be chosen by any particular individual. Sometimes there is the additional assertion that, as the population grows, the probability of an incorrect decision goes to zero. As a consequence of simple properties of common interest games, whenever “sincere” voting leads to the conclusions of the theorem, there are Nash equilibria with these properties. In symmetric environments the equilibria may be taken to be symmetric.

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