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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.

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  • 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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    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. "How proper is the dominance-solvable outcome?," Working Papers hal-01074178, HAL.
    4. 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.
    5. Yukio KORIYAMA & Matias Nunez, 2014. "Hybrid Procedures," THEMA Working Papers 2014-02, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    6. 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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    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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