Universality of Nash Components
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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- McKelvey, Richard D. & McLennan, Andrew, 1997.
"The Maximal Number of Regular Totally Mixed Nash Equilibria,"
Journal of Economic Theory,
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- 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.
- Vermeulen Dries & Jansen Mathijs, 2004. "On the computation of stable sets for bimatrix games," Research Memorandum 020, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Srihari Govindan & Arndt von Schemde & Bernhard von Stengel, 2004. "Symmetry and p-Stability," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(3), pages 359-369, June.
- Demichelis, Stefano & Ritzberger, Klaus, 2003. "From evolutionary to strategic stability," Journal of Economic Theory, Elsevier, vol. 113(1), pages 51-75, November.
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- 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. Full references (including those not matched with items on IDEAS)