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Evolutionary Stochastic Games

Author

Listed:
  • János Flesch
  • Thiruvenkatachari Parthasarathy
  • Frank Thuijsman
  • Philippe Uyttendaele

Abstract

We extend the notion of Evolutionarily Stable Strategies introduced by Maynard Smith and Price (Nature 246:15–18, 1973 ) for models ruled by a single fitness matrix A, to the framework of stochastic games developed by Lloyd Shapley (Proc. Natl. Acad. Sci. USA 39:1095–1100, 1953 ) where, at discrete stages in time, players play one of finitely many matrix games, while the transitions from one matrix game to the next follow a jointly controlled Markov chain. We show that this extension from a single-state model to a multistate model can be done on the assumption of having an irreducible transition law. In a similar way, we extend the notion of Replicator Dynamics introduced by Taylor and Jonker (Math. Biosci. 40:145–156, 1978 ) to the multistate model. These extensions facilitate the analysis of evolutionary interactions that are richer than the ones that can be handled by the original, single-state, evolutionary game model. Several examples are provided. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • János Flesch & Thiruvenkatachari Parthasarathy & Frank Thuijsman & Philippe Uyttendaele, 2013. "Evolutionary Stochastic Games," Dynamic Games and Applications, Springer, vol. 3(2), pages 207-219, June.
    • Handle: RePEc:spr:dyngam:v:3:y:2013:i:2:p:207-219
    DOI: 10.1007/s13235-012-0059-2
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    Cited by:

    1. Sujatha Babu & Nagarajan Krishnamurthy & T. Parthasarathy, 2017. "Stationary, completely mixed and symmetric optimal and equilibrium strategies in stochastic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(3), pages 761-782, August.
    2. K. C. Sivakumar & M. S. Gowda & G. Ravindran & Usha Mohan, 2020. "Preface: International conference on game theory and optimization, June 6–10, 2016, Indian Institute of Technology Madras, Chennai, India," Annals of Operations Research, Springer, vol. 287(2), pages 565-572, April.
    3. 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.
    4. Ezzat Elokda & Saverio Bolognani & Andrea Censi & Florian Dorfler & Emilio Frazzoli, 2021. "Dynamic Population Games: A Tractable Intersection of Mean-Field Games and Population Games," Papers 2104.14662, arXiv.org, revised Jun 2024.

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