Stationary Markov equilibria for K-class discounted stochastic games

Frank Page

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: For a discounted stochastic game with an uncountable state space and compact metric action spaces, we show that if the measurable-selection-valued, Nash payoff selection correspondence of the underlying one-shot game contains a sub-correspondence having the K-limit property (i.e., if the Nash payoff selection sub-correspondence contains its K-limits and therefore is a K correspondence), then the discounted stochastic game has a stationary Markov equilibrium. Our key result is a new fixed point theorem for measurable-selection-valued correspondences having the K-limit property. We also show that if the discounted stochastic game is noisy (Duggan, 2012), or if the underlying probability space satisfies the G-nonatomic condition of Rokhlin (1949) and Dynkin and Evstigneev (1976) (and therefore satisfies the coaser transition kernel condition of He and Sun, 2014), then the Nash payoff selection correspondence contains a sub-correspondence having the K-limit property.

Keywords: approximate Caratheodory selections; fixed points of nonconvex valuedcorrespondences; measurable selection valued correspondences; Komlos limits; Komlos’ Theorem; weak star convergence; discounted stochastic games; stationaryMarkov equilibria. (search for similar items in EconPapers)
JEL-codes: C7 (search for similar items in EconPapers)
Pages: 38 pages
Date: 2015-09-21
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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