IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpga/9805002.html
   My bibliography  Save this paper

Evolutionary Dynamics on Infinite Strategy Spaces

Author

Listed:
  • Joerg Oechssler

    (Humboldt University, Berlin)

  • Frank Riedel

    (Humboldt University)

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 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

  • Joerg Oechssler & Frank Riedel, 1998. "Evolutionary Dynamics on Infinite Strategy Spaces," Game Theory and Information 9805002, University Library of Munich, Germany, revised 05 Aug 1998.
    • Handle: RePEc:wpa:wuwpga:9805002
    Note: pages: 26
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9805/9805002.ps.gz
    Download Restriction: no
    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/game/papers/9805/9805002.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ed Hopkins, "undated". "Price Dispersion: An Evolutionary Approach," Discussion Papers 1996-3, Edinburgh School of Economics, University of Edinburgh.
    2. 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.
    3. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215, April.
    4. 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.
    5. Vega-Redondo, Fernando (ed.), 1996. "Evolution, Games, and Economic Behaviour," OUP Catalogue, Oxford University Press, number 9780198774723.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Dai, Darong, 2010. "The Evolution of Cooperation in a Generalized Moran Process," MPRA Paper 40511, University Library of Munich, Germany.
    3. Christian Korth, 2009. "Reciprocity—An Indirect Evolutionary Analysis," Lecture Notes in Economics and Mathematical Systems, in: Fairness in Bargaining and Markets, chapter 0, pages 35-55, Springer.
    4. 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.
    5. 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.
    6. 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.
    7. 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..
    8. 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.
    9. 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.
    10. Norman, Thomas W.L., 2008. "Dynamically stable sets in infinite strategy spaces," Games and Economic Behavior, Elsevier, vol. 62(2), pages 610-627, March.
    11. Fernando Louge & Frank Riedel, 2012. "Evolutionary Stability in First Price Auctions," Dynamic Games and Applications, Springer, vol. 2(1), pages 110-128, March.
    12. Aviad Heifetz & Yossef Spiegel, 2000. "On the Evolutionary Emergence of Optimism," Econometric Society World Congress 2000 Contributed Papers 1649, Econometric Society.
    13. Knobel, Alexander & Chokaev, Bekhan, 2014. "Possible Economic Outcomes of a Trade Agreement with the European Union," EconStor Preprints 121853, ZBW - Leibniz Information Centre for Economics.
    14. Friedman, Daniel & Ostrov, Daniel N., 2008. "Conspicuous consumption dynamics," Games and Economic Behavior, Elsevier, vol. 64(1), pages 121-145, September.
    15. 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.
    16. Thomas Norman, 2004. "Dynamically Stable Preferences," Economics Series Working Papers 207, University of Oxford, Department of Economics.
    17. 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.
    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.
    21. repec:awi:wpaper:0424 is not listed on IDEAS

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sivan Frenkel & Yuval Heller & Roee Teper, 2018. "The Endowment Effect As Blessing," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(3), pages 1159-1186, August.
    2. Werner Güth & Loreto Erviti & Anthony Ziegelmeyer, 2011. "Asymmetric information without common priors: an indirect evolutionary analysis of quantity competition," Journal of Evolutionary Economics, Springer, vol. 21(5), pages 843-852, December.
    3. John Duffy & Alexander Matros & Ted Temzelides, 2008. "Competitive Behavior in Market Games: Evidence and Theory," Working Paper 366, Department of Economics, University of Pittsburgh, revised Jul 2010.
    4. Sandholm,W.H., 1998. "The evolution of preferences and rapid social change," Working papers 28, Wisconsin Madison - Social Systems.
    5. Roee Teper, 2014. "The Endowment Effect as a Blessing," Working Paper 5862, Department of Economics, University of Pittsburgh.
    6. Christina Pawlowitsch, 2006. "Why evolution does not always lead to an optimal proto-language.An approach based on the replicator dynamics," Vienna Economics Papers 0604, University of Vienna, Department of Economics.
    7. Fanelli, Domenico, 2010. "The Role of Socially Concerned Consumers in the Coexistence of Ethical and Standard Firms," MPRA Paper 20117, University Library of Munich, Germany.
    8. Ajit Mishra, 2004. "Incentives, Norms and the Persistence of Corruption," Dundee Discussion Papers in Economics 161, Economic Studies, University of Dundee.
    9. Friederike Mengel & Veronika Grimm, 2007. "Group Selection With Imperfect Separation - An Experiment," Working Papers. Serie AD 2007-06, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    10. Luciano Andreozzi, 2005. "Hayek Reads the Literature on the Emergence of Norms," Constitutional Political Economy, Springer, vol. 16(3), pages 227-247, September.
    11. William H. Sandholm, 2001. "Preference Evolution, Two-Speed Dynamics, and Rapid Social Change," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(3), pages 637-679, July.
    12. Friederike Mengel, 2006. "A Model Of Immigration, Integration And Cultural Transmission Of Social Norms," Working Papers. Serie AD 2006-08, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    13. Desiree A. Desierto, 2008. "The Dynamics of Economic Integration," DEGIT Conference Papers c013_029, DEGIT, Dynamics, Economic Growth, and International Trade.
    14. Dufwenberg, Martin, 1997. "Some relationships between evolutionary stability criteria in games," Economics Letters, Elsevier, vol. 57(1), pages 45-50, November.
    15. Jose Apesteguia & Miguel Ballester, 2009. "A theory of reference-dependent behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(3), pages 427-455, September.
    16. H Peyton Young, 2014. "The Evolution of Social Norms," Economics Series Working Papers 726, University of Oxford, Department of Economics.
    17. Lichi Zhang & Yanyan Jiang & Junmin Wu, 2022. "Evolutionary Game Analysis of Government and Residents’ Participation in Waste Separation Based on Cumulative Prospect Theory," IJERPH, MDPI, vol. 19(21), pages 1-16, November.
    18. Tom Johnston & Michael Savery & Alex Scott & Bassel Tarbush, 2023. "Game Connectivity and Adaptive Dynamics," Papers 2309.10609, arXiv.org, revised Oct 2024.
    19. Gu, Tianqi & Xu, Weiping & Liang, Hua & He, Qing & Zheng, Nan, 2024. "School bus transport service strategies’ policy-making mechanism – An evolutionary game approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 182(C).
    20. da Silveira, Jaylson Jair & Lima, Gilberto Tadeu, 2021. "Wage inequality as a source of endogenous macroeconomic fluctuations," Structural Change and Economic Dynamics, Elsevier, vol. 56(C), pages 35-52.

    More about this item

    Keywords

    replicator dynamics; evolutionary stability; continuous strategy spaces; oligopoly;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpga:9805002. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: EconWPA (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.