Stationary Markov equilibria for approximable discounted stochastic games

Frank Page

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

Abstract: We identify a new class of uncountable-compact discounted stochastic games for which existence of stationary Markov equilibria can be established and we prove two new existence results for this class. Our approach to proving existence in both cases is new – with both proofs being based upon continuous approximation methods. For our first result we use approximation methods involving measurable-selection-valued continuous functions to establish a new fixed point result for Nash payoff selection correspondences - and more generally for measurable-selection-valued correspondences having nonconvex values. For our second result, we again use approximation methods, but this time involving player action-profile-valued continuous functions to establish a new measurable selection result for upper Caratheodory Nash payoff correspondences. Because conditions which guarantee approximability - the presence of sub-correspondences taking contractible values (or more generally, Rd-values) - are the very conditions which rule out Nash equilibria homeomorphic to the unit circle, we conjecture that for uncountable-compact discounted stochastic games, the approximable class is the widest class for which existence of stationary Markov equilibria can be established.

Keywords: tationary Markov equilibria; discounted stochastic games; fixed point theorem for nonconvex; measurable-selection-valued correspondences; Komlos convergence; weak star convergence; sub-USCOs; contractible values; Rs-values; continuous approximation (search for similar items in EconPapers)
JEL-codes: C7 (search for similar items in EconPapers)
Pages: 49 pages
Date: 2016-08-26
New Economics Papers: this item is included in nep-gth, nep-hpe and nep-ore
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