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Sequential auctions with ambiguity

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  • Ghosh, Gagan
  • Liu, Heng

Abstract

This paper studies sequential auctions in the presence of ambiguity about the distribution of values. Using the multi-self approach to accommodate the possible time inconsistency that arises with dynamic bidding for maxmin bidders, we characterize the unique symmetric and monotone equilibrium in closed form. We show that the equilibrium prices are a supermartingale if the worst-case beliefs reverse hazard rate dominate the true distribution of values, providing an explanation for the well-documented puzzle “declining price anomaly” in sequential auctions. Importantly, the sufficient condition for declining prices allows for dynamic inconsistency. We also propose a non-parametric procedure to identify bidders' values and beliefs from auction data. The model delivers rich testable implications: on the practical side, declining prices imply that bidders' worst-case beliefs first-order stochastically dominate the true distribution of values; on the theoretical side, dynamic inconsistency generates history dependence in bidding strategies and possibly higher revenues for the seller.

Suggested Citation

  • Ghosh, Gagan & Liu, Heng, 2021. "Sequential auctions with ambiguity," Journal of Economic Theory, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:jetheo:v:197:y:2021:i:c:s0022053121001411
    DOI: 10.1016/j.jet.2021.105324
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    Cited by:

    1. Sarah Auster & Christian Kellner, 2023. "Timing Decisions Under Model Uncertainty," CRC TR 224 Discussion Paper Series crctr224_2023_460, University of Bonn and University of Mannheim, Germany.
    2. Sosung Baik & Sung-Ha Hwang, 2021. "Auction design with ambiguity: Optimality of the first-price and all-pay auctions," Papers 2110.08563, arXiv.org.
    3. Sarah Auster & Christian Kellner, 2023. "Timing Decisions under Model Uncertainty," ECONtribute Discussion Papers Series 252, University of Bonn and University of Cologne, Germany.
    4. Sosung Baik & Sung-Ha Hwang, 2022. "Revenue Comparisons of Auctions with Ambiguity Averse Sellers," Papers 2211.12669, arXiv.org.

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    More about this item

    Keywords

    Sequential auctions; Declining prices; Ambiguity; Dynamic inconsistency;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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