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Evolutionary stability of first price auctions

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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. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, Enero-Abr.
    2. 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.
    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.
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    6. 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.
    7. 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.
    8. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    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. 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.
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    Cited by:

    1. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
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    3. 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.
    4. Rabanal, Jean Paul & Lee, Dongwook, 2017. "On the dynamic stability of a price dispersion model using gradient dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 32-42.
    5. Cheung, Man-Wah, 2014. "Pairwise comparison dynamics for games with continuous strategy space," Journal of Economic Theory, Elsevier, vol. 153(C), pages 344-375.

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    Keywords

    Auction theory; Evolutionary stability;

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