Convexity on Nash Equilibria without Linear Structure
To give sucient conditions for Nash Equilibrium existence in a continuous game is a central problem in Game Theory. In this paper, we present two games in which we show how the continuity and quasi-concavity hypotheses are unconnected one to each other. Then, we relax the quasiconcavity assumption by exploiting the multiconnected convexity's concept (Mechaiekh & Others, 1998) in spaces without any linear structure. These results will be applied to two non-zero-sum games lacking the classical assumptions and more recent improvements (Ziad, 1997), (Abalo & Kostreva, 2004). As a minor result, some counterexamples about relationship between some continuity conditions due to Lignola (1997), Reny (1999) and Simon (1995) for Nash equilibria existence are obtained.
|Date of creation:||Jul 2007|
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- Juan Vicente Llinares Císcar, 1995.
"Unified Treatment Of The Problem Of Existence Of Maximal Elements In Binary Relations. A Characterization,"
Working Papers. Serie AD
1995-17, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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- Tian, Guoqiang & Zhou, Jianxin, 1995. "Transfer continuities, generalizations of the Weierstrass and maximum theorems: A full characterization," Journal of Mathematical Economics, Elsevier, vol. 24(3), pages 281-303.
- Nishimura, Kazuo & Friedman, James, 1981. "Existence of Nash Equilibrium in n Person Games without Quasi-Concavity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(3), pages 637-48, October.
- Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," Review of Economic Studies, Oxford University Press, vol. 60(4), pages 935-948.
- Ziad, Abderrahmane, 1999. "Pure strategy Nash equilibria of non-zero-sum two-person games: non-convex case," Economics Letters, Elsevier, vol. 62(3), pages 307-310, March.
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