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Evolutionary dynamics over continuous action spaces for population games that arise from symmetric two-player games

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  • Friedman, Daniel
  • Ostrov, Daniel N.

Abstract

Any absolutely continuous, piecewise smooth, symmetric two-player game can be extended to define a population game in which each player interacts with a large representative subset of the entire population. Assuming that players respond to the payoff gradient over a continuous action space, we obtain nonlinear integro-partial differential equations that are numerically tractable and sometimes analytically tractable. Economic applications include oligopoly, growth theory, and financial bubbles and crashes.

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  • Friedman, Daniel & Ostrov, Daniel N., 2013. "Evolutionary dynamics over continuous action spaces for population games that arise from symmetric two-player games," Journal of Economic Theory, Elsevier, vol. 148(2), pages 743-777.
    • Handle: RePEc:eee:jetheo:v:148:y:2013:i:2:p:743-777
    DOI: 10.1016/j.jet.2012.07.004
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    References listed on IDEAS

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    11. Guercio, Diane Del & Tkac, Paula A., 2002. "The Determinants of the Flow of Funds of Managed Portfolios: Mutual Funds vs. Pension Funds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(4), pages 523-557, December.
    12. Friedman, Daniel & Abraham, Ralph, 2009. "Bubbles and crashes: Gradient dynamics in financial markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 922-937, April.
    13. Nagel, Rosemarie, 1995. "Unraveling in Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 85(5), pages 1313-1326, December.
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    Citations

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    Cited by:

    1. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," Journal of Economic Theory, Elsevier, vol. 162(C), pages 195-208.
    2. Dai Zusai, 2018. "Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution," Papers 1805.04897, arXiv.org, revised May 2019.
    3. Dai Zusai, 2017. "Nonaggregable evolutionary dynamics under payoff heterogeneity," DETU Working Papers 1702, Department of Economics, Temple University.
    4. Mäs, Michael & Nax, Heinrich H., 2016. "A behavioral study of “noise” in coordination games," LSE Research Online Documents on Economics 65422, London School of Economics and Political Science, LSE Library.
    5. Domenico De Giovanni & Fabio Lamantia, 2017. "Evolutionary dynamics of a duopoly game with strategic delegation and isoelastic demand," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 877-903, November.
    6. Cheung, Man-Wah, 2014. "Pairwise comparison dynamics for games with continuous strategy space," Journal of Economic Theory, Elsevier, vol. 153(C), pages 344-375.
    7. Dharini Hingu, 2020. "Asymptotic stability of strongly uninvadable sets," Annals of Operations Research, Springer, vol. 287(2), pages 737-749, April.
    8. Jean Rabanal & Daniel Friedman, 2014. "Incomplete Information, Dynamic Stability and the Evolution of Preferences: Two Examples," Dynamic Games and Applications, Springer, vol. 4(4), pages 448-467, December.
    9. Matthew McGinty, 2021. "Rational conjectures and evolutionary beliefs in public goods games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(6), pages 1130-1143, December.
    10. Rabanal, Jean Paul & Lee, Dongwook, 2017. "On the dynamic stability of a price dispersion model using gradient dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 32-42.
    11. Jean Paul Rabanal, 2017. "On the Evolution of Continuous Types Under Replicator and Gradient Dynamics: Two Examples," Dynamic Games and Applications, Springer, vol. 7(1), pages 76-92, March.
    12. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    13. Dharini Hingu & K. S. Mallikarjuna Rao & A. J. Shaiju, 2018. "Evolutionary Stability of Polymorphic Population States in Continuous Games," Dynamic Games and Applications, Springer, vol. 8(1), pages 141-156, March.
    14. Lai, Chong & Li, Rui & Gao, Xiujuan, 2024. "Bank competition with technological innovation based on evolutionary games," International Review of Economics & Finance, Elsevier, vol. 89(PA), pages 742-759.
    15. M. Ruijgrok & Th. Ruijgrok, 2015. "An Effective Replicator Equation for Games with a Continuous Strategy Set," Dynamic Games and Applications, Springer, vol. 5(2), pages 157-179, June.
    16. Lai, Chong, 2022. "Investment dynamics of fund managers under evolutionary games," International Review of Financial Analysis, Elsevier, vol. 82(C).

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    More about this item

    Keywords

    Population games; Gradient dynamics; Shock waves;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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