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Auctions with Limited Commitment

Author

Listed:
  • Qingmin Liu
  • Konrad Mierendorff
  • Xianwen Shi
Abstract
We study auction design in the standard symmetric independent private values environment, where the seller lacks the commitment power to withhold an unsold object off the market. The seller has a single object and can conduct an infinite sequence of standard auctions with reserve prices to maximize her expected profit. In each period, the seller can commit to a reserve price for the current period but cannot commit to future reserve prices. We analyze the problem with limited commitment through an auxiliary mechanism design problem with full commitment, in which an additional constraint reflects the sequential rationality of the seller. We characterize the maximal profit achievable in any perfect Bayesian equilibrium in the limit as the period length vanishes. The static full commitment profit is not achievable but the seller can always guarantee the profit of an efficient auction. If the number of buyers exceeds a cutoff which is small for many distributions, the efficient auction is optimal. Otherwise, the efficient auction is not optimal, and we give conditions under which the optimal solution consists of an initial auction with a non-trivial reserve price followed by a continuously decreasing price path. The solution is described by a simple ordinary differential equation. Our analysis combines insights from bargaining, auctions, and mechanism design.

Suggested Citation

  • Qingmin Liu & Konrad Mierendorff & Xianwen Shi, 2013. "Auctions with Limited Commitment," Working Papers tecipa-504, University of Toronto, Department of Economics.
    • Handle: RePEc:tor:tecipa:tecipa-504
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    References listed on IDEAS

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    Cited by:

    1. Laura Doval & Vasiliki Skreta, 2022. "Mechanism Design With Limited Commitment," Econometrica, Econometric Society, vol. 90(4), pages 1463-1500, July.
    2. Martino Banchio & Frank Yang, 2021. "Dynamic Pricing with Limited Commitment," Papers 2102.07742, arXiv.org, revised Dec 2021.
    3. Stephan Lauermann & Asher Wolinsky, 2024. "Auctions with Frictions: Recruitment, Entry, and Limited Commitment," ECONtribute Discussion Papers Series 288, University of Bonn and University of Cologne, Germany.
    4. Vitali Gretschko & Martin Pollrich, 2022. "Incomplete Contracts in Multi-period Procurement," Management Science, INFORMS, vol. 68(7), pages 5146-5161, July.
    5. Doval, Laura & Skreta, Vasiliki, 2024. "Optimal mechanism for the sale of a durable good," Theoretical Economics, Econometric Society, vol. 19(2), May.
    6. Santiago R. Balseiro & Omar Besbes & Gabriel Y. Weintraub, 2019. "Dynamic Mechanism Design with Budget-Constrained Buyers Under Limited Commitment," Operations Research, INFORMS, vol. 67(3), pages 711-730, May.
    7. He, Wei & Li, Jiangtao, 2022. "Correlation-robust auction design," Journal of Economic Theory, Elsevier, vol. 200(C).
    8. Chang, Dongkyu & Lee, Jong Jae, 2022. "Price skimming: Commitment and delay in bargaining with outside option," Journal of Economic Theory, Elsevier, vol. 205(C).
    9. Fugger, Nicolas & Gretschko, Vitali & Pollrich, Martin, 2022. "Information design in sequential procurement," Games and Economic Behavior, Elsevier, vol. 135(C), pages 79-85.
    10. Patrick Hummel, 2018. "Reserve prices in repeated auctions," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(1), pages 273-299, March.
    11. Fugger, Nicolas & Gretschko, Vitali & Pollrich, Martin, 2019. "Sequential procurement with limited commitment," ZEW Discussion Papers 19-030, ZEW - Leibniz Centre for European Economic Research.
    12. Ahrash Dianat & Mikhail Freer, 2021. "Credibility in Second-Price Auctions: An Experimental Test," Papers 2105.00204, arXiv.org, revised Jan 2023.
    13. Stephan Lauermann & Asher Wolinsky, 2024. "Auctions with Frictions: Recruitment, Entry, and Limited Commitment," CRC TR 224 Discussion Paper Series crctr224_2024_519, University of Bonn and University of Mannheim, Germany.
    14. Matheus V. X. Ferreira & S. Matthew Weinberg, 2020. "Credible, Truthful, and Two-Round (Optimal) Auctions via Cryptographic Commitments," Papers 2004.01598, arXiv.org, revised May 2020.
    15. Andrew Koh & Sivakorn Sanguanmoo & Kei Uzui, 2024. "Informational Puts," Papers 2411.09191, arXiv.org.
    16. Kirkegaard, René, 2022. "Efficiency in asymmetric auctions with endogenous reserve prices," Games and Economic Behavior, Elsevier, vol. 132(C), pages 234-239.
    17. Ekmekci, Mehmet & Maestri, Lucas, 2022. "Wait or act now? Learning dynamics in stopping games," Journal of Economic Theory, Elsevier, vol. 205(C).
    18. Gretschko, Vitali & Pollrich, Martin, 2019. "Incomplete contracts in dynamic procurement," ZEW Discussion Papers 19-040, ZEW - Leibniz Centre for European Economic Research.
    19. Meryem Essaidi & Matheus V. X. Ferreira & S. Matthew Weinberg, 2022. "Credible, Strategyproof, Optimal, and Bounded Expected-Round Single-Item Auctions for all Distributions," Papers 2205.14758, arXiv.org.

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    More about this item

    Keywords

    Auctions; Commitment; Bargaining; Mechanism Design; Coase Conjecture;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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