Stationary Markov Equilibria

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.

[1]  L. Shapley,et al.  Stochastic Games* , 1953, Proceedings of the National Academy of Sciences.

[2]  J. Doob.  Stochastic processes , 1953 .

[3]  P. Samuelson.  An Exact Consumption-Loan Model of Interest with or without the Social Contrivance of Money , 1958, Journal of Political Economy.

[4]  J. Schwartz,et al.  Linear Operators. Part I: General Theory. , 1960 .

[5]  J. Neveu,et al.  Mathematical foundations of the calculus of probability , 1965 .

[6]  Roy Radner,et al.  Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets , 1972 .

[7]  D. Vere-Jones.  Markov Chains , 1972, Nature.

[8]  T. Bewley.  Existence of equilibria in economies with infinitely many commodities , 1972 .

[9]  Stephen F. LeRoy,et al.  Risk Aversion and the Martingale Property of Stock Prices , 1973 .

[10]  W. Hildenbrand,et al.  Stochastic processes of temporary equilibria , 1974 .

[11]  W. Hildenbrand.  Core and Equilibria of a Large Economy. , 1974 .

[12]  R. Tweedie.  Sufficient conditions for ergodicity and recurrence of Markov chains on a general state space , 1975 .

[13]  O. Hart.  On the optimality of equilibrium when the market structure is incomplete , 1975 .

[14]  R. Lucas.  ASSET PRICES IN AN EXCHANGE ECONOMY , 1978 .

[15]  E. Prescott,et al.  Recursive Competitive Equilibrium: The Case of Homogeneous Households , 1980 .

[16]  Martin Hellwig,et al.  Stochastic processes of temporary equilibria : A note , 1980 .

[17]  W. Whitt.  Representation and Approximation of Noncooperative Sequential Games , 1980 .

[18]  L. Blume.  New techniques for the study of stochastic equilibrium processes , 1982 .

[19]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[20]  T. Parthasarathy.  Existence of equilibrium stationary strategies in discounted stochastic games , 1982 .

[21]  L. Hansen.  Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[22]  Karl Shell,et al.  Do Sunspots Matter? , 1983, Journal of Political Economy.

[23]  Andrzej S. Nowak,et al.  Existence of equilibrium stationary strategies in discounted noncooperative stochastic games with uncountable state space , 1985 .

[24]  J. Tirole.  ASSET BUBBLES AND OVERLAPPING GENERATIONS , 1985 .

[25]  Patrick Billingsley,et al.  Probability and Measure. , 1986 .

[26]  Y. Kifer.  Ergodic theory of random transformations , 1986 .

[27]  Thomas J. Sargent,et al.  Dynamic Macroeconomic Theory , 1987 .

[28]  D. Ryan,et al.  Dynamic Macroeconomic Theory , 1988 .

[29]  S. Sinha,et al.  Existence of stationary equilibrium strategies in non-zero sum discounted stochastic games with uncountable state space and state-independent transitions , 1989 .

[30]  Larry G. Epstein,et al.  Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: A Theoretical Framework , 1989 .

[31]  E. Stacchetti,et al.  Towards a Theory of Discounted Repeated Games with Imperfect Monitoring , 1990 .

[32]  On Stochastic Games with Uncountable State and Action Spaces , 1991 .

[33]  Dan Bernhardt,et al.  Anonymous Sequential Games with General State Space , 1991 .

[34]  Tilman Börgers,et al.  Upper hemicontinuity of the correspondence of subgame-perfect equilibrium outcomes , 1991 .

[35]  R. Sundaram,et al.  SYMMETRIC STOCHASTIC GAMES OF RESOURCE EXTRACTION: THE EXISTENCE OF NON- RANDOMIZED STATIONARY EQUILIBRIUM , 1991 .

[36]  P. Chiappori,et al.  Sunspot Equilibria in Sequential Markets Models , 1991 .

[37]  T. E. S. Raghavan,et al.  Existence of Stationary Correlated Equilibria with Symmetric Information for Discounted Stochastic Games , 1992, Math. Oper. Res..

[38]  Chenghu Ma,et al.  Market equilibrium with heterogeneous recursive-utility-maximizing agents , 1993 .

[39]  Manuel S. Santos,et al.  INCOMPLETE FINANCIAL MARKETS WITH AN INFINITE HORIZON , 1993 .

[40]  M. Quinzii,et al.  Infinite Horizon Incomplete Markets , 1994 .