On the Existence of Equilibria in Discontinuous Games: Three Counterexamples

Guilherme Carmona

Game Theory and Information from University Library of Munich, Germany

Abstract: We study whether we can weaken the conditions given in Reny (1999) and still obtain existence of pure strategy Nash equilibria in quasiconcave normal form games, or, at least, existence of pure strategy $\varepsilon-$equilibria for all epsilon>0. We show by examples that there are: (1) quasiconcave, payoff secure games without pure strategy epsilon-equilibria for small enough epsilon>0 (and hence, without pure strategy Nash equilibria), (2) quasiconcave, reciprocally upper semicontinuous games without pure strategy epsilon-equilibria for small enough epsilon>0, and (3) payoff secure games whose mixed extension is not payoff secure. The last example, due to Sion and Wolfe (1957), also shows that non-quasiconcave games that are payoff secure and reciprocally upper semicontinuous may fail to have mixed strategy equilibria.

Keywords: Discontinuous Games; Nash Equilibrium (search for similar items in EconPapers)
JEL-codes: C73 (search for similar items in EconPapers)
Pages: 11 pages
Date: 2004-02-09
Note: Type of Document - pdf; prepared on winxp; to print on general; pages: 11; figures: 3. none
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Related works:
Journal Article: On the existence of equilibria in discontinuous games: three counterexamples (2005)
Working Paper: On the existence of equilibria in discontinuous games: three counterexamples (2003)
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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpga:0402001

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