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Stability and instability of the unbeatable strategy in dynamic processes

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  • Fuhito Kojima

Abstract

A strategy is unbeatable if it is immune to any entrant strategy of any size. This paper investigates static and dynamic properties of unbeatable strategies. We give equivalent conditions for a strategy to be unbeatable and compare it with related equilibrium concepts. An unbeatable strategy is globally stable under replicator dynamics. In contrast, an unbeatable strategy can fail to be globally stable under best response dynamics even if it is also a unique and strict Nash equilibrium.

Suggested Citation

  • Fuhito Kojima, 2006. "Stability and instability of the unbeatable strategy in dynamic processes," International Journal of Economic Theory, The International Society for Economic Theory, vol. 2(1), pages 41-53, March.
    • Handle: RePEc:bla:ijethy:v:2:y:2006:i:1:p:41-53
    DOI: 10.1111/j.1365-2966.2006.0023.x
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    References listed on IDEAS

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    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
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    Cited by:

    1. Rabah Amir & Igor V. Evstigneev & Valeriya Potapova, 2024. "Unbeatable strategies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(4), pages 891-920, June.
    2. Igor V. Evstigneev & Mohammad Javad Vanaei, 2022. "Evolutionary Behavioural Finance: A Model with Endogenous Asset Payoffs," Economics Discussion Paper Series 2202, Economics, The University of Manchester.
    3. Rabah Amir & Igor Evstigneev & Klaus Schenk-Hoppé, 2013. "Asset market games of survival: a synthesis of evolutionary and dynamic games," Annals of Finance, Springer, vol. 9(2), pages 121-144, May.
    4. Evstigneev, Igor & Hens, Thorsten & Potapova, Valeriya & Schenk-Hoppé, Klaus R., 2020. "Behavioral equilibrium and evolutionary dynamics in asset markets," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 121-135.
    5. Rabah Amir & Igor V. Evstigneev & Valeriya Potapova, 2026. "Unbeatable Strategies in Cournot Duopoly," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(1), pages 1-12, June.
    6. Sergei Belkov & Igor V. Evstigneev & Thorsten Hens, 2020. "An evolutionary finance model with a risk-free asset," Annals of Finance, Springer, vol. 16(4), pages 593-607, December.
    7. Zerong Chen, 2025. "Evolutionary Finance: Models with Long-Lived Assets," Economics Discussion Paper Series 2501, Economics, The University of Manchester.
    8. Zerong Chen, 2024. "Evolutionary Finance: Models with Short-Lived Assets," Economics Discussion Paper Series 2402, Economics, The University of Manchester.
    9. I. V. Evstigneev & T. Hens & M. J. Vanaei, 2023. "Evolutionary finance: a model with endogenous asset payoffs," Journal of Bioeconomics, Springer, vol. 25(2), pages 117-143, August.
    10. Rabah Amir & Igor V. Evstigneev & Mikhail V. Zhitlukhin, 2025. "Contest vs. Competition in Cournot Duopoly: Schaffer's Paradox," Papers 2509.00960, arXiv.org.

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