IDEAS home Printed from https://ideas.repec.org/p/mse/cesdoc/16076rr.html
   My bibliography  Save this paper

Asymptotic value in frequency-dependent games with separable payoffs: a differential approach

Author

Abstract

We study the asymptotic value of a frequency-dependent zero-sum game with separable payoff following a differential approach. The stage payoffs in such games depend on the current actions and on a linear function of the frequency of actions played so far. We associate to the repeated game, in a natural way, a differential game and although the latter presents an irregularity at the origin, we prove that it has a value. We conclude, using appropriate approximations, that the asymptotic value of the original game exists in both the n-stage and the ?-discounted games ant that it coincides with the value of the continuous time game

Suggested Citation

  • Joseph Abdou & Nikolaos Pnevmatikos, 2016. "Asymptotic value in frequency-dependent games with separable payoffs: a differential approach," Documents de travail du Centre d'Economie de la Sorbonne 16076rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jul 2018.
    • Handle: RePEc:mse:cesdoc:16076rr
    as

    Download full text from publisher

    File URL: ftp://mse.univ-paris1.fr/pub/mse/CES2016/16076RR.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Reinoud Joosten & Thomas Brenner & Ulrich Witt, 2003. "Games with frequency-dependent stage payoffs," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(4), pages 609-620, September.
    2. Smale, Steve, 1980. "The Prisoner's Dilemma and Dynamical Systems Associated to Non-Cooperative Games," Econometrica, Econometric Society, vol. 48(7), pages 1617-1634, November.
    3. Bruno Ziliotto, 2016. "A Tauberian Theorem for Nonexpansive Operators and Applications to Zero-Sum Stochastic Games," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1522-1534, November.
    4. Rida Laraki, 2002. "Repeated Games with Lack of Information on One Side: The Dual Differential Approach," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 419-440, May.
    5. Pierre Cardaliaguet & Rida Laraki & Sylvain Sorin, 2012. "A Continuous Time Approach for the Asymptotic Value in Two-Person Zero-Sum Repeated Games," Post-Print hal-00609476, HAL.
    6. Reinoud Joosten, 2004. "Strategic Interaction and Externalities: FD-games and pollution," Papers on Economics and Evolution 2004-17, Philipps University Marburg, Department of Geography.
    7. N. Vieille, 1992. "Weak Approachability," Mathematics of Operations Research, INFORMS, vol. 17(4), pages 781-791, November.
    8. repec:dau:papers:123456789/6775 is not listed on IDEAS
    9. Brenner, Thomas & Witt, Ulrich, 2003. "Melioration learning in games with constant and frequency-dependent pay-offs," Journal of Economic Behavior & Organization, Elsevier, vol. 50(4), pages 429-448, April.
    10. Nicolas Vieille, 1992. "Weak Approachability," Post-Print hal-00481891, HAL.
    Full references (including those not matched with items on IDEAS)

    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. Joseph Abdou & Nikolaos Pnevmatikos, 2016. "Asymptotic value in frequency-dependent games: A differential approach," Documents de travail du Centre d'Economie de la Sorbonne 16076r, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jan 2018.
    2. Pierre Cardaliaguet & Catherine Rainer & Dinah Rosenberg & Nicolas Vieille, 2016. "Markov Games with Frequent Actions and Incomplete Information—The Limit Case," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 49-71, February.
    3. Sylvain Sorin, 2018. "Limit Value of Dynamic Zero-Sum Games with Vanishing Stage Duration," Mathematics of Operations Research, INFORMS, vol. 43(1), pages 51-63, February.
    4. Eilon Solan, 2005. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 51-72, February.
    5. Reinoud Joosten, 2007. "Strategic Advertisement with Externalities: A New Dynamic Approach," Papers on Economics and Evolution 2007-02, Philipps University Marburg, Department of Geography.
    6. Fournier, Gaëtan & Kuperwasser, Eden & Munk, Orin & Solan, Eilon & Weinbaum, Avishay, 2021. "Approachability with constraints," European Journal of Operational Research, Elsevier, vol. 292(2), pages 687-695.
    7. Rad Niazadeh & Negin Golrezaei & Joshua Wang & Fransisca Susan & Ashwinkumar Badanidiyuru, 2023. "Online Learning via Offline Greedy Algorithms: Applications in Market Design and Optimization," Management Science, INFORMS, vol. 69(7), pages 3797-3817, July.
    8. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    9. Vianney Perchet, 2011. "Approachability of Convex Sets in Games with Partial Monitoring," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 665-677, June.
    10. Fabien Gensbittel, 2015. "Extensions of the Cav( u ) Theorem for Repeated Games with Incomplete Information on One Side," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 80-104, February.
    11. Rida Laraki, 2002. "Repeated Games with Lack of Information on One Side: The Dual Differential Approach," Mathematics of Operations Research, INFORMS, vol. 27(2), pages 419-440, May.
    12. Huang, Weihong, 2010. "On the complexity of strategy-switching dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 445-460, September.
    13. Fabien Gensbittel & Jérôme Renault, 2015. "The Value of Markov Chain Games with Incomplete Information on Both Sides," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 820-841, October.
    14. Flesch, János & Laraki, Rida & Perchet, Vianney, 2018. "Approachability of convex sets in generalized quitting games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 411-431.
    15. Ehud Lehrer & Eilon Solan, 2006. "Excludability and Bounded Computational Capacity," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 637-648, August.
    16. Giuseppe Attanasi & Aurora García-Gallego & Nikolaos Georgantzís & Aldo Montesano, 2015. "Bargaining over Strategies of Non-Cooperative Games," Games, MDPI, vol. 6(3), pages 1-26, August.
    17. Reinoud Joosten, 2011. "Social Dilemmas, Time Preferences and Technology Adoption in a Commons Problem," Papers on Economics and Evolution 2011-09, Philipps University Marburg, Department of Geography.
    18. Kalai, Ehud & Stanford, William, 1988. "Finite Rationality and Interpersonal Complexity in Repeated Games," Econometrica, Econometric Society, vol. 56(2), pages 397-410, March.
    19. Pierre Cardaliaguet & Rida Laraki & Sylvain Sorin, 2012. "A Continuous Time Approach for the Asymptotic Value in Two-Person Zero-Sum Repeated Games," Post-Print hal-00609476, HAL.
    20. Sylvain Sorin, 2011. "Zero-Sum Repeated Games: Recent Advances and New Links with Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 172-207, March.

    More about this item

    Keywords

    stochastic game; frequency dependent payoffs; continuous-time game; Hamilton-Jacobi-Bellman-Isaacs equation;
    All these keywords.

    JEL classification:

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:mse:cesdoc:16076rr. 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: Lucie Label (email available below). General contact details of provider: https://edirc.repec.org/data/cenp1fr.html .

    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.