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Universality of Nash Components

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Author Info

  • Dieter Balkenborg

    (Department of Economics, University of Exeter)

  • Dries Vermeulen

    (Department of Quantitative Economics, University Maastricht)

Abstract

We show that Nash equilibrium components are universal for the collection of connected polyhedral sets. More precisely for every polyhedral set we construct a so-called binary game — a common interest game whose common payoff to the players is at most equal to one—whose success set (the set of strategy profiles where the maximal payoff of one is indeed achieved) is homeomorphic to the given polyhedral set. Since compact semi-algebraic sets can be triangulated, a similar result follows for the collection of connected compact semi-algebraic sets.

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File URL: http://people.exeter.ac.uk/cc371/RePEc/dpapers/DP1205.pdf
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Bibliographic Info

Paper provided by Exeter University, Department of Economics in its series Discussion Papers with number 1205.

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Date of creation: 2012
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Handle: RePEc:exe:wpaper:1205

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Keywords: Strategic form games; Nash equilibrium; Nash component; topology.;

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  1. DEMICHELIS, Stefano & RITZBERGER, Klaus, 2000. "From evolutionary to strategic stability," CORE Discussion Papers 2000059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Vermeulen, Dries & Jansen, Mathijs, 2005. "On the computation of stable sets for bimatrix games," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 735-763, September.
  3. McKelvey, Richard D. & McLennan, Andrew, 1997. "The Maximal Number of Regular Totally Mixed Nash Equilibria," Journal of Economic Theory, Elsevier, vol. 72(2), pages 411-425, February.
  4. Balkenborg, Dieter & Schlag, Karl H., 2007. "On the evolutionary selection of sets of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 133(1), pages 295-315, March.
  5. Srihari Govindan & Arndt von Schemde & Bernhard von Stengel, 2004. "Symmetry and p-Stability," International Journal of Game Theory, Springer, vol. 32(3), pages 359-369, 06.
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