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Generic Finiteness of Equilibrium Distributions for Bimatrix Outcome Game Forms

Author

Listed:
  • Litan, Cristian

    (Universitatea Banes-Bolyai, Cluj-Napoca)

  • Marhuenda, Francisco

    (University Carlos II of Madrid)

  • Sudhölter, Peter

    (Department of Business and Economics)

Abstract

We provide sufficient and necessary conditions for the generic finiteness of the number of distributions on outcomes, induced by the completely mixed Nash equilibria associated to a bimatrix outcome game form. These equivalent conditions are stated in terms of the ranks of two matrices constructed from the original game form.

Suggested Citation

  • Litan, Cristian & Marhuenda, Francisco & Sudhölter, Peter, 2017. "Generic Finiteness of Equilibrium Distributions for Bimatrix Outcome Game Forms," Discussion Papers on Economics 7/2017, University of Southern Denmark, Department of Economics.
    • Handle: RePEc:hhs:sdueko:2017_007
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    File URL: http://www.sdu.dk/-/media/files/om_sdu/institutter/ivoe/disc_papers/disc_2017/dpbe7_2017.pdf?la=da
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    References listed on IDEAS

    as
    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. 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.
    3. 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.
    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. 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.
    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. 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.
    8. 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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    Cited by:

    1. Michel Grabisch & Hervé Moulin & José Manuel Zarzuelo, 2024. "Professor Peter Sudhölter (1957–2024)," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 289-294, June.

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    More about this item

    Keywords

    Outcome game form; Completely mixed Nash equilibrium; Generic finiteness;
    All these keywords.

    JEL classification:

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

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