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Domain L-Majorization and Equilibrium Existence in Discontinuous Games

Pavlo Prokopovych

No 31, Discussion Papers from Kyiv School of Economics

Abstract: We study the equilibrium existence problem in normal form and qualitative games in which it is possible to associate with each nonequilibrium point an open neighborhood and a collection of deviation strategies such that, at any nonequilibrium point of the neighborhood, a player can increase her payoff by switching to the deviation strategy designated for her. An equilibrium existence theorem for compact, quasiconcave games with two players is established. We propose a new form of the better-reply security condition, called the strong single deviation property, that covers games whose set of Nash equilibria is not necessarily closed. We introduce domain L-majorized correspondences and use them to study equilibrium existence in qualitative games.

Keywords: Majorized correspondence; Qualitative game; Discontinuous game; Better-reply security; Single deviation property (search for similar items in EconPapers)
JEL-codes: C65 C72 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-gth
Date: 2010-07, Revised 2011-05
Note: Revised and resubmitted to Economic Theory
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http://repec.kse.org.ua/pdf/KSE_dp31.pdf Revised version, May 2011 (application/pdf)

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