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Generic finiteness of equilibrium payoffs for bimatrix games

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  • Mas-Colell, Andreu

Abstract

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

Suggested Citation

  • Mas-Colell, Andreu, 2010. "Generic finiteness of equilibrium payoffs for bimatrix games," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 382-383, July.
    • Handle: RePEc:eee:mateco:v:46:y:2010:i:4:p:382-383
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    References listed on IDEAS

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    1. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    2. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    3. 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.
    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. Philippe Bich & Julien Fixary, 2021. "Structure and oddness theorems for pairwise stable networks," Post-Print halshs-03287524, HAL.
    6. Fixary, Julien, 2025. "Unknottedness of graphs of pairwise stable networks & network dynamics," Journal of Mathematical Economics, Elsevier, vol. 120(C).
    7. 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.
    8. 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.
    9. 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.
    10. 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:

    • C - Mathematical and Quantitative Methods
    • D - Microeconomics

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