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On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms

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  • Govindan, Srihari
  • McLennan, Andrew

Abstract

Consider nonempty finite pure strategy sets S[subscript 1], . . . , S[subscript n], let S = S[subscript 1] times . . . times S[subscript n], let Omega be a finite space of "outcomes," let Delta(Omega) be the set of probability distributions on Omega, and let theta: S approaches Delta(Omega) be a function. We study the conjecture that for any utility in a generic set of n-tuples of utilities on Omega there are finitely many distributions on Omega induced by the Nash equilibria of the game given by the induced utilities on S. We give a counterexample refuting the conjecture for n >= 3. Several special cases of the conjecture follow from well-known theorems, and we provide some generalizations of these results.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 69 (2001)
Issue (Month): 2 (March)
Pages: 455-71

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Handle: RePEc:ecm:emetrp:v:69:y:2001:i:2:p:455-71

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Cited by:
  1. De Sinopoli, Francesco & Pimienta, Carlos, 2010. "Costly network formation and regular equilibria," Games and Economic Behavior, Elsevier, vol. 69(2), pages 492-497, July.
  2. Carlos Pimienta, 2007. "Generic Determinacy of Nash Equilibrium in Network Formation Games," Discussion Papers 2007-31, School of Economics, The University of New South Wales.
  3. Govindan, Srihari & Wilson, Robert B., 2007. "Stable Outcomes of Generic Games in Extensive Form," Research Papers 1933r, Stanford University, Graduate School of Business.
  4. Carlos Pimienta, 2007. "Generic Finiteness of Outcome Distributions for Two Person Game Forms with Three Outcomes," Discussion Papers 2007-20, School of Economics, The University of New South Wales.
  5. Francesco De Sinopoli & Giovanna Iannantuoni, 2003. "On the Generic Strategic Stability of Nash Equilibria if Voting is Costly," CEIS Research Paper 41, Tor Vergata University, CEIS.
  6. DE SINOPOLI, Francesco, 1998. "Two results about generic non cooperative voting games with plurality rule," CORE Discussion Papers 1998034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Hans Haller & Roger Lagunoff, 2000. "Genericity and Markovian Behavior in Stochastic Games," Econometrica, Econometric Society, vol. 68(5), pages 1231-1248, September.
  8. DE SINOPOLI, Francesco, 1999. "Further remarks on strategic stability in plurality games," CORE Discussion Papers 1999030, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Mas-Colell, Andreu, 2010. "Generic finiteness of equilibrium payoffs for bimatrix games," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 382-383, July.
  10. Andreu Mas-Colell, 2008. "Generic finiteness of equilibrium payoffs for bimatrix games," Economics Working Papers 1103, Department of Economics and Business, Universitat Pompeu Fabra.
  11. In-Uck Park, 1993. "Generic Finiteness of Equilibrium Outcome Distributions in Sender-Received Cheap-Talk Games," Game Theory and Information 9310002, EconWPA.
  12. Litan, Cristian M. & Marhuenda, Francisco, 2012. "Determinacy of equilibrium outcome distributions for zero sum and common utility games," Economics Letters, Elsevier, vol. 115(2), pages 152-154.

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