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State-Policy Dynamics in Evolutionary Games

Author

Listed:
  • Ilaria Brunetti

    (University of Avignon)

  • Yezekael Hayel

    (University of Avignon)

  • Eitan Altman

    (INRIA Sophia Antipolis and LINCS - Laboratory of Information, Network and Communication Sciences)

Abstract

Standard evolutionary game theory framework is a useful tool to study large interacting systems and to understand the strategic behavior of individuals in such complex systems. Adding an individual state to model local feature of each player in this context allows one to study a wider range of problems in various application areas as networking, biology, etc. In this paper, we introduce such an extension of evolutionary game framework and particularly, we focus on the dynamical aspects of this system. Precisely, we study the coupled dynamics of the policies and the individual states inside a population of interacting individuals. We first define a general model by coupling replicator dynamics and continuous-time Markov decision processes, and we then consider a particular case of a two policies and two states evolutionary game. We first obtain a system of combined dynamics, and we show that the rest points of this system are equilibria profiles of our evolutionary game with individual state dynamics. Second, by assuming two different timescales between states and policies dynamics, we can compute explicitly the equilibria. Then, by transforming our evolutionary game with individual states into a standard evolutionary game, we obtain an equilibrium profile which is equivalent, in terms of occupation measures and expected fitness to the previous one. All our results are illustrated with numerical analysis.

Suggested Citation

  • Ilaria Brunetti & Yezekael Hayel & Eitan Altman, 2018. "State-Policy Dynamics in Evolutionary Games," Dynamic Games and Applications, Springer, vol. 8(1), pages 93-116, March.
    • Handle: RePEc:spr:dyngam:v:8:y:2018:i:1:d:10.1007_s13235-016-0208-0
    DOI: 10.1007/s13235-016-0208-0
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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. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    3. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    4. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
    5. János Flesch & Thiruvenkatachari Parthasarathy & Frank Thuijsman & Philippe Uyttendaele, 2013. "Evolutionary Stochastic Games," Dynamic Games and Applications, Springer, vol. 3(2), pages 207-219, June.
    6. Piotr Więcek & Eitan Altman, 2015. "Stationary Anonymous Sequential Games with Undiscounted Rewards," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 686-710, August.
    7. 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. Jianhua Zhu & Julien S. Baker & Zhiting Song & Xiao-Guang Yue & Wenqi Li, 2023. "Government regulatory policies for digital transformation in small and medium-sized manufacturing enterprises: an evolutionary game analysis," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-18, December.
    2. Shutian Liu & Yuhan Zhao & Quanyan Zhu, 2022. "Herd Behaviors in Epidemics: A Dynamics-Coupled Evolutionary Games Approach," Dynamic Games and Applications, Springer, vol. 12(1), pages 183-213, March.
    3. Ezzat Elokda & Andrea Censi & Saverio Bolognani, 2021. "Dynamic population games," Papers 2104.14662, arXiv.org.
    4. Zhi-Hua Hu & Shu-Wen Wang, 2022. "An Evolutionary Game Model Between Governments and Manufacturers Considering Carbon Taxes, Subsidies, and Consumers’ Low-Carbon Preference," Dynamic Games and Applications, Springer, vol. 12(2), pages 513-551, June.
    5. Wang, Jie & He, Ya-qun & Wang, Heng-guang & Wu, Ru-fei, 2023. "Low-carbon promotion of new energy vehicles: A quadrilateral evolutionary game," Renewable and Sustainable Energy Reviews, Elsevier, vol. 188(C).

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