Parameterized state-contingent games, 3M minimal Nash correspondences, and connectedness

Jing Fu and Frank Page

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

Abstract: Under mild assumptions on primitives, we show that all parameterized state-contingent games (PSGs) have upper Caratheodory (uC) Nash (equilibrium) correspondences which contain minimal uC Nash correspondences having the 3M property (defined here). This implies that all PSGs have Nash correspondences made up of minimal uC Nash correspondences taking closed, connected, and essential Nash equilibrium values (essential in the sense of Fort, 1950). It then follows from Fu and Page (2022b), that because all PSGs have continuum valued minimal Nash correspondences, all PSGs have Caratheodory approximable Nash payoff correspondences - which in turn implies that all PSGs have approximable Nash payoff selection correspondences, and therefore have Nash payoff selection correspondences with fixed points.

Keywords: m-tuples of Caratheodory functions; upper Caratheodory correspondences; continuum valued upper Caratheodory sub-correspondences; weak star upper semicontinuous measurable selection valued correspondences; approximate Caratheodory selections; fixed points of nonconvex; measurable selection valued correspondences induced by the composition of an m-tuple of Caratheodory functions with a continuum valued upper Caratheodory sub-correspondence (search for similar items in EconPapers)
JEL-codes: C00 C70 (search for similar items in EconPapers)
Pages: 27 pages
Date: 2022-03-25
New Economics Papers: this item is included in nep-gth
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Citations: View citations in EconPapers (1)

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