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Generic finiteness of outcome distributions for two-person game forms with three outcomes

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  • Pimienta, Carlos

Abstract

A two-person game form is given by nonempty finite sets S1, S2 of pure strategies, a nonempty set [Omega] of outcomes, and a function [theta]:S1xS2-->[Delta]([Omega]), where [Delta]([Omega]) is the set of probability measures on [Omega]. We prove that if the set of outcomes contains just three elements, generically, there are finitely many distributions on [Omega] induced by Nash equilibria.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matsoc:v:59:y:2010:i:3:p:364-365
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    References listed on IDEAS

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    1. Pimienta, Carlos, 2009. "Generic determinacy of Nash equilibrium in network-formation games," Games and Economic Behavior, Elsevier, vol. 66(2), pages 920-927, July.
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    4. 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.
    5. De Sinopoli, Francesco, 2001. "On the Generic Finiteness of Equilibrium Outcomes in Plurality Games," Games and Economic Behavior, Elsevier, vol. 34(2), pages 270-286, February.
    6. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-794, July.
    7. Govindan, Srihari & Wilson, Robert, 2001. "Direct Proofs of Generic Finiteness of Nash Equilibrium Outcomes," Econometrica, Econometric Society, vol. 69(3), pages 765-769, May.
    8. Park, In-Uck, 1997. "Generic Finiteness of Equilibrium Outcome Distributions for Sender-Receiver Cheap-Talk Games," Journal of Economic Theory, Elsevier, vol. 76(2), pages 431-448, October.
    9. Kukushkin, Nicolai S. & Litan, Cristian M. & Marhuenda, Francisco, 2007. "On the generic finiteness of outcome distributions for bimatrix game forms," UC3M Working papers. Economics we073520, Universidad Carlos III de Madrid. Departamento de Economía.
    10. Mas-Colell, Andreu, 2010. "Generic finiteness of equilibrium payoffs for bimatrix games," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 382-383, July.
    11. 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.
    12. 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.
    13. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
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    Cited by:

    1. 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.
    2. 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.
    3. Yukio KORIYAMA & Matias Nunez, 2014. "Hybrid Procedures," THEMA Working Papers 2014-02, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    4. Yukio Koriyama & Matias Nunez, 2014. "How proper is the dominance-solvable outcome?," Working Papers hal-01074178, HAL.
    5. 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.
    6. Cristian Litan & Francisco Marhuenda & Peter Sudhölter, 2020. "Generic finiteness of equilibrium distributions for bimatrix outcome game forms," Annals of Operations Research, Springer, vol. 287(2), pages 801-810, April.

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    More about this item

    Keywords

    Generic finiteness Game forms Nash equilibrium;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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