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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. 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.
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    3. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
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    5. Saran, R.R.S. & Serrano, R., 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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    Cited by:

    1. 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.
    2. Cheung, Man-Wah, 2014. "Pairwise comparison dynamics for games with continuous strategy space," Journal of Economic Theory, Elsevier, vol. 153(C), pages 344-375.
    3. 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.
    4. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    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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