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On superiority and weak stability of population states in evolutionary games

Author

Listed:
  • Dharini Hingu

    (Indian Institute of Technology, Madras)

  • K. S. Mallikarjuna Rao

    (Indian Institute of Technology, Bombay)

  • A. J. Shaiju

    (Indian Institute of Technology, Madras)

Abstract

We revisit some concepts of superiority and weak stability of population states in evolutionary games with continuous strategy space. We prove a general stability result for replicator trajectories by introducing the concept of superiority with respect to a given closed set. Some important results in the literature regarding weak stability turn out to be special cases of our main result.

Suggested Citation

  • Dharini Hingu & K. S. Mallikarjuna Rao & A. J. Shaiju, 2020. "On superiority and weak stability of population states in evolutionary games," Annals of Operations Research, Springer, vol. 287(2), pages 751-760, April.
    • Handle: RePEc:spr:annopr:v:287:y:2020:i:2:d:10.1007_s10479-018-2971-3
    DOI: 10.1007/s10479-018-2971-3
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    References listed on IDEAS

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    1. 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.
    2. Matthijs Veelen & Peter Spreij, 2009. "Evolution in games with a continuous action space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 355-376, June.
    3. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, December.
    4. Carlos Alós-Ferrer, 2006. "The Discretization Of Continuum Strategy Spaces," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 499-514.
    5. Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
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