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Evolution in games with a continuous action space

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  • Matthijs Veelen
  • Peter Spreij

Abstract

This discussion paper resulted in a publication in 'Economic Theory' , 2009, 39(3), 355-376. Allowing for games with a continuous action space, we deal with the question whether and when static conceptslike evolutionary stability can shed any light on what happens in the dynamical context of a population playingthese games. The continuous equivalents of theorems for the finite case are either harder to prove or simplyuntrue. In some cases that fall within the latter category, sensible additional assumptions can repair the damage.Apart from that it turns out that we can no longer ignore the mutation process; with a continuous action space itmakes quite a difference what kind of shocks we consider to be likely.
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Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:39:y:2009:i:3:p:355-376
    DOI: 10.1007/s00199-008-0338-8
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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. J. Hofbauer & P. Schuster & K. Sigmund, 2010. "A Note on Evolutionary Stable Strategies and Game Dynamics," Levine's Working Paper Archive 441, David K. Levine.
    4. 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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    Citations

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    Cited by:

    1. 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.
    2. Aslihan Akdeniz & Christopher Graser & Matthijs van Veelen, 2020. "Homo Moralis and regular altruists – preference evolution for when they disagree," Tinbergen Institute Discussion Papers 20-062/I, Tinbergen Institute.
    3. Akdeniz, Aslıhan & van Veelen, Matthijs, 2023. "Evolution and the ultimatum game," Games and Economic Behavior, Elsevier, vol. 142(C), pages 570-612.
    4. 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.
    5. van Veelen, Matthijs & García, Julián, 2019. "In and out of equilibrium II: Evolution in repeated games with discounting and complexity costs," Games and Economic Behavior, Elsevier, vol. 115(C), pages 113-130.
    6. Konrad Podczeck & Daniela Puzzello, 2012. "Independent random matching," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 50(1), pages 1-29, May.
    7. Matthijs van Veelen & Benjamin Allen & Moshe Hoffman & Burton Simon & Carl Veller, 2016. "Inclusive Fitness," Tinbergen Institute Discussion Papers 16-055/I, Tinbergen Institute.
    8. Aradhana Narang & A. J. Shaiju, 2019. "Evolutionary Stability of Polymorphic Profiles in Asymmetric Games," Dynamic Games and Applications, Springer, vol. 9(4), pages 1126-1142, December.
    9. Karl D. Lewis & A. J. Shaiju, 2024. "Asymmetric Replicator Dynamics on Polish Spaces: Invariance, Stability, and Convergence," Dynamic Games and Applications, Springer, vol. 14(5), pages 1160-1190, November.
    10. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    11. García, Julián & van Veelen, Matthijs, 2016. "In and out of equilibrium I: Evolution of strategies in repeated games with discounting," Journal of Economic Theory, Elsevier, vol. 161(C), pages 161-189.
    12. Dharini Hingu & K. S. Mallikarjuna Rao & A. J. Shaiju, 2018. "Evolutionary Stability of Polymorphic Population States in Continuous Games," Dynamic Games and Applications, Springer, vol. 8(1), pages 141-156, March.

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    More about this item

    Keywords

    Evolutionary stability; Uniform invasion barrier; Local superiority; Asymptotic stability; Continuous action space; Topology; C70;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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