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Evolutionary Stability of First Price Auctions

  • Fernando Louge

    (Institute of Mathematical Economics, Bielefeld University)

  • Frank Riedel


    (Institute of Mathematical Economics, Bielefeld University)

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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Paper provided by Center for Mathematical Economics, Bielefeld University in its series Center for Mathematical Economics 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. Oechssler, Jorg & Riedel, Frank, 2002. "On the Dynamic Foundation of Evolutionary Stability in Continuous Models," Journal of Economic Theory, Elsevier, vol. 107(2), pages 223-252, December.
  2. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721.
  3. 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.
  4. Josef Hofbauer & Jörg Oechssler, 2005. "Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case," Working Papers 0424, University of Heidelberg, Department of Economics, revised Dec 2005.
  5. Oechssler, Joerg & Frank Riedel, 1999. "Evolutionary Dynamics on Infinite Strategy Spaces," Discussion Paper Serie A 606, University of Bonn, Germany.
  6. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
  7. Hon-Snir, Shlomit & Monderer, Dov & Sela, Aner, 1998. "A Learning Approach to Auctions," Journal of Economic Theory, Elsevier, vol. 82(1), pages 65-88, September.
  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. Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
  10. 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.
  11. Fernando Louge, 2010. "On the Stability of CSS under the Replicator Dynamic," Center for Mathematical Economics Working Papers 436, Center for Mathematical Economics, Bielefeld University.
  12. 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.
  13. 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).
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