Domain L-Majorization and Equilibrium Existence in Discontinuous Games

27 Pages Posted: 6 Jul 2010 Last revised: 3 Jun 2011

Date Written: June 1, 2011

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: Better-reply secure game, Discontinuous game, Single deviation property, Majorized correspondence, Qualitative game

JEL Classification: C65, C72

Suggested Citation

Prokopovych, Pavlo, Domain L-Majorization and Equilibrium Existence in Discontinuous Games (June 1, 2011). Available at SSRN: https://ssrn.com/abstract=1632250 or http://dx.doi.org/10.2139/ssrn.1632250

Pavlo Prokopovych (Contact Author)

Kyiv School of Economics ( email )

vul. Yakira, 13, 3d floor, suite 334
Kyiv, 04119
Ukraine

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