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Evolutionary Dynamics on Infinite Strategy Spaces

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Author Info
Oechssler, Joerg
Frank Riedel

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Abstract

The study of evolutionary dynamics was so far mainly restricted to finite strategy spaces. In this paper we show that this unsatisfying restriction is unnecessary. We specify a simple condition under which the continuous time replicator dynamics are well defined for the case of infinte strategy spaces. Furthermore, we provide new conditions for the stability of rest points and show that even strict equilibria may be unstable. Finally, we apply this general theory to a number of applications like the Nash demand game, the War of Attrition, linear-quadratic games, the harvest preemption game, and games with mixed strategies.

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File URL: ftp://web.bgse.uni-bonn.de/pub/RePEc/bon/bonsfa/bonsfa606.pdf
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Publisher Info
Paper provided by University of Bonn, Germany in its series Discussion Paper Serie A with number 606.

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Length: 31 pages
Date of creation: Nov 1999
Date of revision:
Handle: RePEc:bon:bonsfa:606

Contact details of provider:
Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 9221
Web page: http://www.bgse.uni-bonn.de/index.php?id=517

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Related research
Keywords: replicator dynamics; evolutionary stability; continuous strategy spaces;

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Find related papers by 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

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Steffen Huck & Georg Kirchsteiger & Jörg Oechssler, 2003. "Learning to Like What You Have - Explaining the Endowment Effect," Bonn Econ Discussion Papers bgse5_2003, University of Bonn, Germany. [Downloadable!]
    Other versions:
  2. Ed Hopkins, . "Price Dispersion: An Evolutionary Approach," Department of Economics 1996 : III, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
    Other versions:
  3. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Hofbauer, Josef & Oechssler, Jörg & Riedel, Frank, 2005. "Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case," Sonderforschungsbereich 504 Publications 05-41, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
    Other versions:
  2. Aviad Heifetz & Yossi Spiegel, 2000. "On the Evolutionary Emergence of Optimism," Discussion Papers 1304, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  3. Aviad Heifetz & Chris Shannon & Yossi Spiegel, 2002. "What to Maximize If You Must," Department of Economics, Working Paper Series 1052, Department of Economics, Institute for Business and Economic Research, UC Berkeley. [Downloadable!]
    Other versions:
  4. Siegfried Berninghaus & Christian Korth & Stefan Napel, 2007. "Reciprocity—an indirect evolutionary analysis," Journal of Evolutionary Economics, Springer, vol. 17(5), pages 579-603, October. [Downloadable!] (restricted)
    Other versions:
  5. Thomas Norman, 2004. "Dynamically Stable Preferences," Economics Series Working Papers 207, University of Oxford, Department of Economics. [Downloadable!]
  6. Julide Yazar, 2006. "Evolving densities in continuous strategy games through particle simulations," Journal of Economic Interaction and Coordination, Springer, vol. 1(2), pages 171-187, November. [Downloadable!] (restricted)
  7. Steffen Huck & Georg Kirchsteiger & Jörg Oechssler, 2003. "Learning to Like What You Have - Explaining the Endowment Effect," Bonn Econ Discussion Papers bgse5_2003, University of Bonn, Germany. [Downloadable!]
    Other versions:
  8. Dirk Bergemann & Karl Schlag, 2005. "Robust Monopoly Pricing: The Case of Regret," Economics Working Papers ECO2005/10, European University Institute. [Downloadable!]
  9. Heifetz, Aviad & Spiegel, Yossi, 2000. "On the Evolutionary Emergency of Optimism," Working Papers 1104, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  10. 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. [Downloadable!]
  11. Dirk Bergemann & Karl Schlag, 2007. "Robust Monopoly Pricing," Levine's Bibliography 321307000000000983, UCLA Department of Economics. [Downloadable!]
    Other versions:
  12. Aviad Heifetz & Yossef Spiegel, 2000. "On the Evolutionary Emergence of Optimism," Econometric Society World Congress 2000 Contributed Papers 1649, Econometric Society. [Downloadable!]
  13. Younghwan In, 2005. "A Fictitious-Play Model of Bargaining To Implement the Nash Solution," Departmental Working Papers wp0509, National University of Singapore, Department of Economics. [Downloadable!]
  14. Aviad Heifetz & Chris Shannon & Yossi Spiegel, 2005. "The Dynamic Evolution of Preferences," Discussion Papers 1415, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
    Other versions:
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