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Multiple-Object, Discriminatory Auctions with Bidding Constraints: A Game-Theoretic Analysis

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  • Thomas R. Palfrey

    (California Institute of Technology)

Abstract

This paper examines the existence and characterization of pure strategy Nash equilibria in multiple-object auction games in which buyers face a binding constraint on exposure. There are five major results. First, symmetric Nash equilibria exist if and only if there are two or less buyers and two or less items. Second, a Nash equilibrium may not exist if the seller sets a positive reservation bid. Third, asymmetric solutions to symmetrically parameterized games typically involve "high-low" strategies: each buyer submits positive bids only on some restricted subset of the items. Fourth, Nash equilibria typically generate zero "surplus" to the buyers. Fifth, when asymmetric solutions exist and the buyers are identical, these solutions are never unique.

Suggested Citation

  • Thomas R. Palfrey, 1980. "Multiple-Object, Discriminatory Auctions with Bidding Constraints: A Game-Theoretic Analysis," Management Science, INFORMS, vol. 26(9), pages 935-946, September.
    • Handle: RePEc:inm:ormnsc:v:26:y:1980:i:9:p:935-946
    DOI: 10.1287/mnsc.26.9.935
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    Cited by:

    1. Simon Finster, 2020. "Strategic Bidding in Product-Mix, Sequential, and Simultaneous Auctions," Economics Papers 2020-W03, Economics Group, Nuffield College, University of Oxford.
    2. Gerard van der Laan & Zaifu Yang, 2016. "An ascending multi-item auction with financially constrained bidders," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 109-149, December.
    3. Pitchik, Carolyn, 2009. "Budget-constrained sequential auctions with incomplete information," Games and Economic Behavior, Elsevier, vol. 66(2), pages 928-949, July.
    4. Longstaff, Francis A & Han, Bing & Merrill, Craig, 2004. "Revenue Implications of Multi-Item Multi-Unit Auction Designs: Empirical Evidence from the U.S. Treasury Buyback Auctions," University of California at Los Angeles, Anderson Graduate School of Management qt7344v866, Anderson Graduate School of Management, UCLA.
    5. Ganesh Iyer & Amit Pazgal, 2008. "Procurement bidding with restrictions," Quantitative Marketing and Economics (QME), Springer, vol. 6(2), pages 177-204, June.
    6. Anne-Christine Barthel & Tarun Sabarwal, 2018. "Directional monotone comparative statics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(3), pages 557-591, October.
    7. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    8. repec:kan:wpaper:201502 is not listed on IDEAS
    9. Lewis, Tracy R. & Sappington, David E. M., 1995. "Using markets to allocate pollution permits and other scarce resource rights under limited information," Journal of Public Economics, Elsevier, vol. 57(3), pages 431-455, July.
    10. repec:kan:wpaper:201412 is not listed on IDEAS
    11. Schnitzlein, Charles R. & Shao, Minjie, 2013. "Capacity constraints and the winner's curse in multi-unit common value auctions," The Quarterly Review of Economics and Finance, Elsevier, vol. 53(2), pages 188-201.
    12. Gagan Ghosh, 2015. "Non-existence of equilibria in simultaneous auctions with a common budget-constraint," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 253-274, May.
    13. Elena Katok & Alvin E. Roth, 2004. "Auctions of Homogeneous Goods with Increasing Returns: Experimental Comparison of Alternative "Dutch" Auctions," Management Science, INFORMS, vol. 50(8), pages 1044-1063, August.
    14. Ghosh, Gagan, 2021. "Simultaneous auctions with budgets: Equilibrium existence and characterization," Games and Economic Behavior, Elsevier, vol. 126(C), pages 75-93.

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    Keywords

    games: bidding;

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