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Evolutionary Stability of First Price Auctions

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  • Fernando Louge

    (Institute of Mathematical Economics, Bielefeld University)

  • Frank Riedel

    ()
    (Institute of Mathematical Economics, Bielefeld University)

Abstract

This paper studies the evolutionary stability of the unique Nash equilibrium of a first price sealed bid auction. It is shown that the Nash equilibrium is not asymptotically stable under payoff monotonic dynamics for arbitrary initial popu- lations. In contrast, when the initial population includes a continuum of strategies around the equilibrium, the replicator dynamic does converge to the Nash equilibrium. Simulations are presented for the replicator and Brown-von Neumann-Nash dynamics. They suggest that the convergence for the replicator dynamic is slow compared to the Brown-von Neumann-Nash dynamics.

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File URL: http://www.imw.uni-bielefeld.de/papers/files/imw-wp-435.pdf
File Function: First version, 2010
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Bibliographic Info

Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 435.

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Length: 14 pages
Date of creation: Jun 2010
Date of revision:
Handle: RePEc:bie:wpaper:435

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  1. 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.
  2. Monderer, Dov & Shlomit Hon-Snir & Aner Sela, 1996. "A Learning Approach to Auctions," Discussion Paper Serie B 388, University of Bonn, Germany.
  3. Fernando Louge, 2010. "On the Stability of CSS under the Replicator Dynamic," Working Papers 436, Bielefeld University, Center for Mathematical Economics.
  4. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521551847, October.
  5. Joerg Oechssler & Frank Riedel, 1998. "Evolutionary Dynamics on Infinite Strategy Spaces," Game Theory and Information 9805002, EconWPA, revised 12 May 1998.
  6. Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers 028, ESRC Centre on Economics Learning and Social Evolution.
  7. Jörg Oechssler & Frank Riedel, 2000. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Bonn Econ Discussion Papers bgse7_2000, University of Bonn, Germany.
  8. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer, vol. 19(1), pages 59-89.
  9. Ross Cressman, 2009. "Continuously stable strategies, neighborhood superiority and two-player games with continuous strategy space," International Journal of Game Theory, Springer, vol. 38(2), pages 221-247, June.
  10. Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
  11. Saran Rene & Serrano Roberto, 2010. "Ex-Post Regret Learning in Games with Fixed and Random Matching: The Case of Private Values," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  12. repec:wop:humbsf:1998-68 is not listed on IDEAS
  13. 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.
  14. K. Schlag, 2010. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Levine's Working Paper Archive 454, David K. Levine.
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Cited by:
  1. Metzger, Lars Peter, 2014. "Invader strategies in the war of attrition with private information," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 160-166.

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