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Generic finiteness of equilibrium payoffs for bimatrix games

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Abstract

It is shown that in any affine space of payoff matrices the equilibrium payoffs of bimatrix games are generically finite.

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  • Andreu Mas-Colell, 2008. "Generic finiteness of equilibrium payoffs for bimatrix games," Economics Working Papers 1103, Department of Economics and Business, Universitat Pompeu Fabra.
    • Handle: RePEc:upf:upfgen:1103
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    References listed on IDEAS

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    1. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    2. 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.
    3. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    4. van Damme, E.E.C., 1983. "Refinements of the Nash Equilibrium Concept," Other publications TiSEM 116b3ec4-be4d-48c2-ad1b-8, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Bich, Philippe & Fixary, Julien, 2022. "Network formation and pairwise stability: A new oddness theorem," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    2. Lonnie Turpin, 2023. "A Unique Mixed Equilibrium Payoff in Quantum Bimatrix Games," Journal of Optimization Theory and Applications, Springer, vol. 196(3), pages 1119-1124, March.
    3. Philippe Bich & Julien Fixary, 2021. "Structure and oddness theorems for pairwise stable networks," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-03287524, HAL.
    4. 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.
    5. 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.
    6. Bich, Philippe & Fixary, Julien, 2024. "Oddness of the number of Nash equilibria: The case of polynomial payoff functions," Games and Economic Behavior, Elsevier, vol. 145(C), pages 510-525.
    7. Philippe Bich & Julien Fixary, 2021. "Structure and oddness theorems for pairwise stable networks," Post-Print halshs-03287524, HAL.
    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.
    9. 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

    Bimatrix Games; Generic Finiteness;

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • D - Microeconomics

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