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Evolution in games with a continuous action space

  • Matthijs Veelen

    ()

  • Peter Spreij

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.

(This abstract was borrowed from another version of this item.)

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File URL: http://hdl.handle.net/10.1007/s00199-008-0338-8
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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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  1. Joerg Oechssler & Frank Riedel, 2000. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Game Theory and Information 0004004, EconWPA.
  2. Joerg Oechssler & Frank Riedel, 1998. "Evolutionary Dynamics on Infinite Strategy Spaces," Game Theory and Information 9805002, EconWPA, revised 12 May 1998.
  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. 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.
  5. Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
  6. 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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