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Numerical Analysis of Asymmetric First Price Auctions

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  • Wayne-Roy Gayle

Abstract

We develop a powerful and user-friendly program for numerically solving first price auction problems where an arbitrary number of bidders draw independent valuations from heterogenous distributions and the auctioneer imposes a reserve price for the object. The heterogeneity in this model arises both from the specification of ex-ante heterogenous, non-uniform distributions of private values for bidders, as well as the possibility of subsets of these bidders colluding. The technique extends the work of Marshall, Meurer, Richard, and Stromquist (1994), where they applied backward recursive Taylor series expansion techniques to solve two-player asymmetric first price auctions under uniform distributions. The algorithm is also used to numerically investigate whether revenue equivalence between first price and second price auctions in symmetric models extend to the asymmetric case. In particular, we simulate the model under various environments and find evidence that under the assumption of first order stochastic dominance, the first price auction generates higher expected revenue to the seller, while the second price auction is more susceptible to collusive activities. However, when the assumption of first order stochastic dominance is relaxed, and the distributions of private values cross once, the evidence suggests that the second price auction may in some cases generate higher expected revenue to the seller

Suggested Citation

  • Wayne-Roy Gayle, 2005. "Numerical Analysis of Asymmetric First Price Auctions," Computing in Economics and Finance 2005 472, Society for Computational Economics.
  • Handle: RePEc:sce:scecf5:472
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    File URL: http://repec.org/sce2005/up.18137.1108489875.pdf
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    References listed on IDEAS

    as
    1. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    2. Matthews, Steven A., 1983. "Selling to risk averse buyers with unobservable tastes," Journal of Economic Theory, Elsevier, vol. 30(2), pages 370-400, August.
    3. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    4. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
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    More about this item

    Keywords

    Asymetric; Optimal Reserve; Ex-ante Heterogeneity;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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