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Simultaneous 2nd price item auctions with no-underbidding

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  • Feldman, Michal
  • Shabtai, Galia

Abstract

The literature on the Price of Anarchy (PoA) of simple auctions employs a no-overbidding assumption but has completely overlooked the no-underbidding phenomenon, which is evident in empirical studies on variants of the second price auction. In this work, we provide a theoretical foundation for the no-underbidding phenomenon. We study the PoA of simultaneous 2nd price auctions (S2PA) under a new natural condition of no underbidding, meaning that agents never bid on items less than their marginal values. We establish improved (mostly tight) bounds on the PoA of S2PA under no-underbidding for different valuation classes, in both full-information and incomplete information settings. Specifically, we show that the PoA is at least 1/2 for general monotone valuations, which extends to Bayesian PoA with arbitrary correlated distributions. We also establish a tight PoA bound of 2/3 for S2PA with XOS valuations, under no-overbidding and no-underbidding, which extends to Bayesian PoA with independent distributions.

Suggested Citation

  • Feldman, Michal & Shabtai, Galia, 2023. "Simultaneous 2nd price item auctions with no-underbidding," Games and Economic Behavior, Elsevier, vol. 140(C), pages 316-340.
    • Handle: RePEc:eee:gamebe:v:140:y:2023:i:c:p:316-340
    DOI: 10.1016/j.geb.2023.03.009
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    References listed on IDEAS

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    1. DavidJ. Cooper & Hanming Fang, 2008. "Understanding Overbidding In Second Price Auctions: An Experimental Study," Economic Journal, Royal Economic Society, vol. 118(532), pages 1572-1595, October.
    2. Kagel, John H & Levin, Dan, 1993. "Independent Private Value Auctions: Bidder Behaviour in First-, Second- and Third-Price Auctions with Varying Numbers of Bidders," Economic Journal, Royal Economic Society, vol. 103(419), pages 868-879, July.
    3. Andreas Roider & Patrick W. Schmitz, 2012. "Auctions with Anticipated Emotions: Overbidding, Underbidding, and Optimal Reserve Prices," Scandinavian Journal of Economics, Wiley Blackwell, vol. 114(3), pages 808-830, September.
    4. Lehmann, Benny & Lehmann, Daniel & Nisan, Noam, 2006. "Combinatorial auctions with decreasing marginal utilities," Games and Economic Behavior, Elsevier, vol. 55(2), pages 270-296, May.
    5. Dütting, Paul & Henzinger, Monika & Starnberger, Martin, 2018. "Valuation compressions in VCG-based combinatorial auctions," LSE Research Online Documents on Economics 87419, London School of Economics and Political Science, LSE Library.
    6. Ronald Harstad, 2000. "Dominant Strategy Adoption and Bidders' Experience with Pricing Rules," Experimental Economics, Springer;Economic Science Association, vol. 3(3), pages 261-280, December.
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