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

Fu, Jing and Page, Frank (2022) Parameterized state-contingent games, 3M minimal Nash correspondences, and connectedness. Systemic Risk Centre Discussion Papers (116). Systemic Risk Centre, The London School of Economics and Political Science, London, UK.

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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.

Item Type:	Monograph (Discussion Paper)
Official URL:	https://www.systemicrisk.ac.uk/
Additional Information:	© 2022 The Author(s)
Divisions:	Systemic Risk Centre
Subjects:	H Social Sciences > HC Economic History and Conditions H Social Sciences > HG Finance
JEL classification:	C - Mathematical and Quantitative Methods > C0 - General > C00 - General C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C70 - General
Date Deposited:	05 Jun 2023 15:12
Last Modified:	16 Sep 2023 00:00
URI:	http://eprints.lse.ac.uk/id/eprint/118877

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