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A General Structure Theorem for the Nash Equilibrium Correspondence

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Author Info
Predtetchinski,Arkadi (METEOR)
Abstract

I consider n-person normal form games where the strategy set of every player is a non-empty compact convex subset of Euclidean space, and the payoff function of player i is continuous and concave in player i''s own strategies. No further restrictions (such as multilinearity of the payoff fucntions or the requirements that the strategy sets be polyhedral) are imposed. In this setting we demonstrate that the graph of the nash equilibrium correspondence is homeomorphic to the space of games. This result generalizes a well-known structure theorem of Kohlberg and Mertens[6].

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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 023.

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Date of creation: 2004
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Handle: RePEc:dgr:umamet:2004023

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Keywords: mathematical economics;

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  1. Demichelis, Stefano & Germano, Fabrizio, 2002. "On (un)knots and dynamics in games," Games and Economic Behavior, Elsevier, vol. 41(1), pages 46-60, October. [Downloadable!] (restricted)
  2. Zhou, Yuqing, 1997. "Genericity Analysis on the Pseudo-Equilibrium Manifold," Journal of Economic Theory, Elsevier, vol. 73(1), pages 79-92, March. [Downloadable!] (restricted)
  3. DeMichelis, Stefano & Germano, Fabrizio, 2000. "Some consequences of the unknottedness of the Walras correspondence," Journal of Mathematical Economics, Elsevier, vol. 34(4), pages 537-545, December. [Downloadable!] (restricted)
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  4. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September. [Downloadable!] (restricted)
  5. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-94, July. [Downloadable!] (restricted)
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  6. Balasko, Yves, 1978. "Economic Equilibrium and Catastrophe Theory: An Introduction," Econometrica, Econometric Society, vol. 46(3), pages 557-69, May. [Downloadable!] (restricted)
  7. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-69, May.
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