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Evolutionary dynamics on infinite strategy spaces

Author

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  • Oechssler, Jörg
  • Riedel, Frank

Abstract

The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this restriction is in most cases unnecessary. We give a mild condition under which the continuous time replicator dynamics are well defined for infinite strategy spaces. Furthermore, we provide conditions for the stability of rest points. Finally, we apply this general theory to a number of applications like the Nash demand game, the War of Attrition, Cournot and Bertrand oligopoly games, and mixed strategies.

Suggested Citation

  • Oechssler, Jörg & Riedel, Frank, 1998. "Evolutionary dynamics on infinite strategy spaces," SFB 373 Discussion Papers 1998,68, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:199868
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    References listed on IDEAS

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    1. Steffen Huck & Georg Kirchsteiger & Jörg Oechssler, 2005. "Learning to like what you have - explaining the endowment effect," Economic Journal, Royal Economic Society, vol. 115(505), pages 689-702, July.
    2. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, January.
    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. Steffen Huck & Georg Kirchsteiger & Jörg Oechssler, 2005. "Learning to like what you have - explaining the endowment effect," Economic Journal, Royal Economic Society, vol. 115(505), pages 689-702, July.
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    Cited by:

    1. Dai, Darong, 2010. "一般化Moran过程中的合作演化
      [The Evolution of Cooperation in a Generalized Moran Process]
      ," MPRA Paper 40261, University Library of Munich, Germany.
    2. Friedman, Daniel & Ostrov, Daniel N., 2008. "Conspicuous consumption dynamics," Games and Economic Behavior, Elsevier, vol. 64(1), pages 121-145, September.
    3. Heifetz, Aviad & Shannon, Chris & Spiegel, Yossi, 2007. "What to maximize if you must," Journal of Economic Theory, Elsevier, vol. 133(1), pages 31-57, March.
    4. Dai, Darong, 2010. "The Evolution of Cooperation in a Generalized Moran Process," MPRA Paper 40511, University Library of Munich, Germany.
    5. Ed Hopkins & Robert M. Seymour, 2002. "The Stability of Price Dispersion under Seller and Consumer Learning," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(4), pages 1157-1190, November.
    6. Siegfried Berninghaus & Christian Korth & Stefan Napel, 2007. "Reciprocity—an indirect evolutionary analysis," Journal of Evolutionary Economics, Springer, vol. 17(5), pages 579-603, October.
    7. Ross Cressman & Josef Hofbauer & Frank Riedel, 2005. "Stability of the Replicator Equation for a Single-Species with a Multi-Dimensional Continuous Trait Space," Bonn Econ Discussion Papers bgse12_2005, University of Bonn, Germany.
    8. Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2009. "Brown-von Neumann-Nash dynamics: The continuous strategy case," Games and Economic Behavior, Elsevier, vol. 65(2), pages 406-429, March.
    9. Aviad Heifetz & Chris Shannon & Yossi Spiegel, 2007. "The Dynamic Evolution of Preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(2), pages 251-286, August.
    10. Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2009. "Brown-von Neumann-Nash dynamics: The continuous strategy case," Games and Economic Behavior, Elsevier, vol. 65(2), pages 406-429, March.
    11. Thomas Norman, 2004. "Dynamically Stable Preferences," Economics Series Working Papers 207, University of Oxford, Department of Economics.
    12. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters,in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441 World Scientific Publishing Co. Pte. Ltd..
    13. Fernando Louge & Frank Riedel, 2012. "Evolutionary Stability in First Price Auctions," Dynamic Games and Applications, Springer, vol. 2(1), pages 110-128, March.
    14. Ely, Jeffrey C. & Sandholm, William H., 2005. "Evolution in Bayesian games I: Theory," Games and Economic Behavior, Elsevier, vol. 53(1), pages 83-109, October.
    15. Warneryd, Karl, 2002. "Rent, risk, and replication: Preference adaptation in winner-take-all markets," Games and Economic Behavior, Elsevier, vol. 41(2), pages 344-364, November.
    16. Heifetz, Aviad & Shannon, Chris & Spiegel, Yossi, 2002. "What to Maximize If You Must," Department of Economics, Working Paper Series qt0hj6631n, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
    17. Norman, Thomas W.L., 2008. "Dynamically stable sets in infinite strategy spaces," Games and Economic Behavior, Elsevier, vol. 62(2), pages 610-627, March.
    18. Heifetz, Aviad & Segev, Ella, 2004. "The evolutionary role of toughness in bargaining," Games and Economic Behavior, Elsevier, vol. 49(1), pages 117-134, October.
    19. Julide Yazar, 2006. "Evolving densities in continuous strategy games through particle simulations," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 1(2), pages 171-187, November.
    20. Stegeman, Mark & Rhode, Paul, 2004. "Stochastic Darwinian equilibria in small and large populations," Games and Economic Behavior, Elsevier, vol. 49(1), pages 171-214, October.

    More about this item

    Keywords

    replicator dynamics; evolutionary stability; continuous strategy spaces; oligopoly;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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