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Evolutionary stability of first price auctions

Author

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  • Louge, Fernando

    (Center for Mathematical Economics, Bielefeld University)

  • Riedel, Frank

    (Center for 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 populations. 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.

Suggested Citation

  • Louge, Fernando & Riedel, Frank, 2011. "Evolutionary stability of first price auctions," Center for Mathematical Economics Working Papers 435, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:435
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    References listed on IDEAS

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    1. 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.
    2. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, May.
    3. Rene Saran & Roberto Serrano, 2010. "Ex-post regret learning in games with fixed and random matching: The case of private values," Working Papers 2010-11, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    4. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    5. JÃrg Oechssler & Frank Riedel, 2001. "Evolutionary dynamics on infinite strategy spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), 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.
    7. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    8. 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.
    9. Louge, Fernando, 2011. "On the stability of CSS under the replicator dynamic," Center for Mathematical Economics Working Papers 436, Center for Mathematical Economics, Bielefeld University.
    10. 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.
    11. Ross Cressman, 2009. "Continuously stable strategies, neighborhood superiority and two-player games with continuous strategy space," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 221-247, June.
    12. Cressman, Ross, 2005. "Stability of the replicator equation with continuous strategy space," Mathematical Social Sciences, Elsevier, vol. 50(2), pages 127-147, September.
    13. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
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    Cited by:

    1. repec:eee:dyncon:v:84:y:2017:i:c:p:32-42 is not listed on IDEAS
    2. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    3. Cheung, Man-Wah, 2014. "Pairwise comparison dynamics for games with continuous strategy space," Journal of Economic Theory, Elsevier, vol. 153(C), pages 344-375.
    4. 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.
    5. Saran, Rene & Serrano, Roberto, 2014. "Ex-post regret heuristics under private values (I): Fixed and random matching," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 97-111.

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    Keywords

    Auction theory; Evolutionary stability;

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