[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v99y2016icp206-223.html
   My bibliography  Save this article

Imitative dynamics for games with continuous strategy space

Author

Listed:
  • Cheung, Man-Wah
Abstract
This paper studies imitative dynamics for games with continuous strategy space. We define imitative dynamics—which include the replicator dynamic as a special case—as evolutionary dynamics that satisfy the imitative property and payoff monotonicity. Our definition of payoff monotonicity, which we use Radon–Nikodym derivatives to define, is weaker than the one proposed in Oechssler and Riedel (2002). We find that Oechssler and Riedel (2002)'s definition is too strong, and our definition is more adequate than theirs. We show that for a broad class of payoff functional dynamics, payoff monotonicity à la Oechssler and Riedel (2002) is equivalent to aggregate monotonicity in the sense of Samuelson and Zhang (1992). We then provide sufficient conditions for imitative dynamics and general evolutionary dynamics to be well-defined. Finally, with our definition of payoff monotonicity, a number of results that are standard for finite games extend to the case of games with continuous strategy space.

Suggested Citation

  • Cheung, Man-Wah, 2016. "Imitative dynamics for games with continuous strategy space," Games and Economic Behavior, Elsevier, vol. 99(C), pages 206-223.
    • Handle: RePEc:eee:gamebe:v:99:y:2016:i:c:p:206-223
    DOI: 10.1016/j.geb.2016.08.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825616300793
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2016.08.003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
    2. Oechssler, Jorg & Riedel, Frank, 2002. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Journal of Economic Theory, Elsevier, vol. 107(2), pages 223-252, December.
    3. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-1399, November.
    4. Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2009. "Brown-von Neumann-Nash dynamics: The continuous strategy case," Games and Economic Behavior, Elsevier, vol. 65(2), pages 406-429, March.
    5. Friedman, Daniel, 1991. "Evolutionary Games in Economics," Econometrica, Econometric Society, vol. 59(3), pages 637-666, May.
    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. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    8. Lahkar, Ratul & Riedel, Frank, 2015. "The logit dynamic for games with continuous strategy sets," Games and Economic Behavior, Elsevier, vol. 91(C), pages 268-282.
    9. Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cheung, Man-Wah & Lahkar, Ratul, 2018. "Nonatomic potential games: the continuous strategy case," Games and Economic Behavior, Elsevier, vol. 108(C), pages 341-362.
    2. Lahkar, Ratul & Mukherjee, Saptarshi, 2019. "Evolutionary implementation in a public goods game," Journal of Economic Theory, Elsevier, vol. 181(C), pages 423-460.
    3. Jiabin Wu, 2021. "Stochastic Value Formation," Dynamic Games and Applications, Springer, vol. 11(3), pages 597-611, September.
    4. Cheung, Man-Wah & Wu, Jiabin, 2018. "On the probabilistic transmission of continuous cultural traits," Journal of Economic Theory, Elsevier, vol. 174(C), pages 300-323.
    5. Sarvesh Bandhu & Ratul Lahkar, 2021. "Implementation in Large Population Games with Multiple Equilibria," Working Papers 62, Ashoka University, Department of Economics.
    6. Sarvesh Bandhu & Ratul Lahkar, 2023. "Evolutionary robustness of dominant strategy implementation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 685-721, August.
    7. Lahkar, Ratul & Mukherjee, Saptarshi, 2021. "Evolutionary implementation in aggregative games," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 137-151.
    8. Georgiy Karev, 2020. "Dynamics of Strategy Distributions in a One-Dimensional Continuous Trait Space for Games with a Quadratic Payoff Function," Games, MDPI, vol. 11(1), pages 1-12, March.
    9. Lahkar, Ratul & Mukherjee, Sayan & Roy, Souvik, 2023. "The logit dynamic in supermodular games with a continuum of strategies: A deterministic approximation approach," Games and Economic Behavior, Elsevier, vol. 139(C), pages 133-160.
    10. Ratul Lahkar & Vinay Ramani, 2022. "An Evolutionary Approach to Pollution Control in Competitive Markets," Dynamic Games and Applications, Springer, vol. 12(3), pages 872-896, September.
    11. Ratul Lahkar & Vinay Ramani, 2021. "An Evolutionary Approach to Pollution Control in Competitive Markets," Working Papers 68, Ashoka University, Department of Economics.
    12. Wenjun Hu & Haiyan Tian & Gang Zhang, 2019. "Bifurcation Analysis of Three-Strategy Imitative Dynamics with Mutations," Complexity, Hindawi, vol. 2019, pages 1-8, October.
    13. 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.
    14. Ratul Lahkar, 2020. "Convergence to Walrasian equilibrium with minimal information," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(3), pages 553-578, July.
    15. Karl D. Lewis & A. J. Shaiju, 2024. "Asymmetric Replicator Dynamics on Polish Spaces: Invariance, Stability, and Convergence," Dynamic Games and Applications, Springer, vol. 14(5), pages 1160-1190, November.
    16. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    17. Jacquot, Paulin & Wan, Cheng, 2022. "Nonatomic aggregative games with infinitely many types," European Journal of Operational Research, Elsevier, vol. 301(3), pages 1149-1165.
    18. Lahkar, Ratul & Mukherjee, Sayan & Roy, Souvik, 2022. "Generalized perturbed best response dynamics with a continuum of strategies," Journal of Economic Theory, Elsevier, vol. 200(C).
    19. Ratul Lahkar & Sayan Mukherjee & Souvik Roy, 2022. "A Deterministic Approximation Approach to the Continuum Logit Dynamic with an Application to Supermodular Games," Working Papers 79, Ashoka University, Department of Economics.
    20. RatulLahkar & Sayan Mukherjee & Souvik Roy, 2021. "Generalized Perturbed Best Response Dynamics with a Continuum of Strategies," Working Papers 51, Ashoka University, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    2. 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.
    3. Ratul Lahkar & Vinay Ramani, 2022. "An Evolutionary Approach to Pollution Control in Competitive Markets," Dynamic Games and Applications, Springer, vol. 12(3), pages 872-896, September.
    4. Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2009. "Brown-von Neumann-Nash dynamics: The continuous strategy case," Games and Economic Behavior, Elsevier, vol. 65(2), pages 406-429, March.
    5. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    6. Cheung, Man-Wah & Lahkar, Ratul, 2018. "Nonatomic potential games: the continuous strategy case," Games and Economic Behavior, Elsevier, vol. 108(C), pages 341-362.
    7. Dharini Hingu, 2020. "Asymptotic stability of strongly uninvadable sets," Annals of Operations Research, Springer, vol. 287(2), pages 737-749, April.
    8. Ratul Lahkar & Vinay Ramani, 2021. "An Evolutionary Approach to Pollution Control in Competitive Markets," Working Papers 68, Ashoka University, Department of Economics.
    9. Lahkar, Ratul & Mukherjee, Saptarshi, 2021. "Evolutionary implementation in aggregative games," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 137-151.
    10. Lahkar, Ratul & Mukherjee, Saptarshi, 2019. "Evolutionary implementation in a public goods game," Journal of Economic Theory, Elsevier, vol. 181(C), pages 423-460.
    11. Sarvesh Bandhu & Ratul Lahkar, 2023. "Evolutionary robustness of dominant strategy implementation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 685-721, August.
    12. 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.
    13. Lahkar, Ratul & Riedel, Frank, 2015. "The logit dynamic for games with continuous strategy sets," Games and Economic Behavior, Elsevier, vol. 91(C), pages 268-282.
    14. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    15. Lahkar, Ratul, 2019. "Elimination of non-individualistic preferences in large population aggregative games," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 150-165.
    16. Lahkar, Ratul & Mukherjee, Sayan & Roy, Souvik, 2022. "Generalized perturbed best response dynamics with a continuum of strategies," Journal of Economic Theory, Elsevier, vol. 200(C).
    17. Ratul Lahkar, 2020. "Convergence to Walrasian equilibrium with minimal information," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(3), pages 553-578, July.
    18. Sarvesh Bandhu & Ratul Lahkar, 2021. "Implementation in Large Population Games with Multiple Equilibria," Working Papers 62, Ashoka University, Department of Economics.
    19. Aradhana Narang & A. J. Shaiju, 2021. "Stability of faces in asymmetric evolutionary games," Annals of Operations Research, Springer, vol. 304(1), pages 343-359, September.
    20. Karl D. Lewis & A. J. Shaiju, 2024. "Asymmetric Replicator Dynamics on Polish Spaces: Invariance, Stability, and Convergence," Dynamic Games and Applications, Springer, vol. 14(5), pages 1160-1190, November.

    More about this item

    Keywords

    Imitative dynamics; Replicator dynamic; Payoff monotonicity; Continuous strategy space;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:99:y:2016:i:c:p:206-223. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.