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Games with frequency-dependent stage payoffs

Author

Listed:
  • Reinoud Joosten
  • Thomas Brenner
  • Ulrich Witt

Abstract

Games with frequency-dependent stage payoffs (FD-games), are infinitely repeated non-cooperative games played at discrete moments in time called stages. The stage payoffs depend on the action pair actually chosen, and on the relative frequencies with which all actions were chosen before. We assume that players wish to maximize their expected (limiting) average rewards over the entire time-horizon. We prove an analogy to, as well as an extension of the (perfect) Folk Theorem. Each pair of rewards in the convex hull of all individually-rational jointly-convergent pure-strategy rewards can be supported by an equilibrium. Moreover, each pair of rewards in same set giving each player strictly more than the threat-point-reward, can be supported by a subgame-perfect equilibrium. Under a pair of jointly-convergent strategies, the relative frequency of each action pair converges in the long run. Copyright Springer-Verlag Heidelberg 2003

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jogath:v:31:y:2003:i:4:p:609-620
    DOI: 10.1007/s001820300143
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    Citations

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    Cited by:

    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 16076, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Joseph M. Abdou & Nikolaos Pnevmatikos, 2019. "Asymptotic Value in Frequency-Dependent Games with Separable Payoffs: A Differential Approach," Dynamic Games and Applications, Springer, vol. 9(2), pages 295-313, June.
    3. Huang, Weihong, 2010. "On the complexity of strategy-switching dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 75(3), pages 445-460, September.
    4. 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.
    5. Reinoud Joosten, 2007. "Patience, Fish Wars, rarity value & Allee effects," Papers on Economics and Evolution 2007-24, Philipps University Marburg, Department of Geography.
    6. Werner Güth & Hartmut Kliemt & Stefan Napel, 2006. "Population-Dependent Costs of Detecting Trustworthiness - An Indirect Evolutionary Analysis -," Papers on Strategic Interaction 2006-08, Max Planck Institute of Economics, Strategic Interaction Group.
    7. Juan Vidal-Puga, 2017. "On the effect of taxation in the online sports betting market," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 8(2), pages 145-175, June.
    8. Reinoud Joosten & Robin Meijboom, 2010. "Stochastic games with endogenous transitions," Papers on Economics and Evolution 2010-24, Philipps University Marburg, Department of Geography.
    9. Reinoud Joosten, 2014. "Social dilemmas, time preferences and technology adoption in a commons problem," Journal of Bioeconomics, Springer, vol. 16(3), pages 239-258, October.
    10. Reinoud Joosten, 2007. "Strategic Advertisement with Externalities: A New Dynamic Approach," Papers on Economics and Evolution 2007-02, Philipps University Marburg, Department of Geography.
    11. Reinoud Joosten, 2016. "Strong and Weak Rarity Value: Resource Games with Complex Price–Scarcity Relationships," Dynamic Games and Applications, Springer, vol. 6(1), pages 97-111, March.

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