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Evolution in games with a continuous action space

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  • Matthijs Veelen

    ()

  • Peter Spreij

Abstract

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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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 39 (2009)
Issue (Month): 3 (June)
Pages: 355-376

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Handle: RePEc:spr:joecth:v:39:y:2009:i:3:p:355-376

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Related research

Keywords: Evolutionary stability; Uniform invasion barrier; Local superiority; Asymptotic stability; Continuous action space; Topology; C70;

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  1. Matthijs Veelen & Peter Spreij, 2009. "Evolution in games with a continuous action space," Economic Theory, Springer, vol. 39(3), pages 355-376, June.
  2. Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
  3. Oechssler, Jörg & Riedel, Frank, 2000. "On the dynamic foundation of evolutionary stability in continuous models," SFB 373 Discussion Papers 2000,73, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  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. JÃrg Oechssler & Frank Riedel, 2001. "Evolutionary dynamics on infinite strategy spaces," Economic Theory, Springer, vol. 17(1), pages 141-162.
  6. 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.
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Cited by:
  1. Konrad Podczeck & Daniela Puzzello, 2012. "Independent random matching," Economic Theory, Springer, vol. 50(1), pages 1-29, May.
  2. Matthijs van Veelen, 2001. "Evolution in Games with a Continuous Action Space," Tinbergen Institute Discussion Papers 01-068/1, Tinbergen Institute.

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