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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.

Suggested Citation

  • Govindan, Srihari & McLennan, Andrew, 2001. "On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms," Econometrica, Econometric Society, vol. 69(2), pages 455-471, March.
  • Handle: RePEc:ecm:emetrp:v:69:y:2001:i:2:p:455-71
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    Cited by:

    1. Meroni, Claudia & Pimienta, Carlos, 2017. "The structure of Nash equilibria in Poisson games," Journal of Economic Theory, Elsevier, vol. 169(C), pages 128-144.
    2. Pimienta, Carlos, 2009. "Generic determinacy of Nash equilibrium in network-formation games," Games and Economic Behavior, Elsevier, vol. 66(2), pages 920-927, July.
    3. 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).
    4. Francesco Sinopoli & Giovanna Iannantuoni, 2005. "On the generic strategic stability of Nash equilibria if voting is costly," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 25(2), pages 477-486, February.
    5. Litan, Cristian & Marhuenda, Francisco & Sudhölter, Peter, 2015. "Determinacy of equilibrium in outcome game forms," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 28-32.
    6. Mas-Colell, Andreu, 2010. "Generic finiteness of equilibrium payoffs for bimatrix games," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 382-383, July.
    7. Hans Haller & Roger Lagunoff, 2000. "Genericity and Markovian Behavior in Stochastic Games," Econometrica, Econometric Society, vol. 68(5), pages 1231-1248, September.
    8. Pimienta, Carlos, 2010. "Generic finiteness of outcome distributions for two-person game forms with three outcomes," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 364-365, May.
    9. Govindan, Srihari & Wilson, Robert B., 2007. "Stable Outcomes of Generic Games in Extensive Form," Research Papers 1933r, Stanford University, Graduate School of Business.
    10. De Sinopoli, Francesco & Pimienta, Carlos, 2010. "Costly network formation and regular equilibria," Games and Economic Behavior, Elsevier, vol. 69(2), pages 492-497, July.
    11. Kukushkin, Nikolai S. & Litan, Cristian M. & Marhuenda, Francisco, 2008. "On the generic finiteness of equilibrium outcome distributions in bimatrix game forms," Journal of Economic Theory, Elsevier, vol. 139(1), pages 392-395, March.
    12. In-Uck Park, 1993. "Generic Finiteness of Equilibrium Outcome Distributions in Sender-Received Cheap-Talk Games," Game Theory and Information 9310002, EconWPA.
    13. 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).
    14. Yukio KORIYAMA & Matias Nunez, 2014. "Hybrid Procedures," THEMA Working Papers 2014-02, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    15. 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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    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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