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Commitment in first-price auctions

Author

Listed:
  • Yunjian Xu

    (Chinese University of Hong Kong)

  • Katrina Ligett

    (Hebrew University
    California Institute of Technology)

Abstract

We study a variation of the single-item sealed-bid first-price auction wherein one bidder (the leader) publicly commits to a (possibly mixed) strategy before the others submit their bids. For the case wherein all bidders’ valuations are commonly known, we fully characterize the committed mixed strategy that is optimal for the leader and find that both the leader and the follower with the highest valuation strictly benefit from the commitment, so long as the leader’s valuation is strictly higher than the second highest valuation of the followers. We further show that compared with the simultaneous first-price auction, the leader’s optimal commitment yields the same net utility benefit to both of these bidders. As a result, the two highest valued bidders’ incentives are aligned, facilitating coordination and implementation of the commitment. Finally, we provide characterization of the leader’s optimal commitment in a Bayesian setting with two bidders, leveraging the methodology developed for the complete-information setting.

Suggested Citation

  • Yunjian Xu & Katrina Ligett, 2018. "Commitment in first-price auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 449-489, August.
    • Handle: RePEc:spr:joecth:v:66:y:2018:i:2:d:10.1007_s00199-017-1069-5
    DOI: 10.1007/s00199-017-1069-5
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    Cited by:

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    2. Cuihong Fan & Byoung Heon Jun & Elmar G. Wolfstetter, 2023. "Spying and imperfect commitment in first-price auctions: a case of tacit collusion," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(2), pages 255-275, October.
    3. Sinitsyn, Maxim, 2022. "Price leadership with promotions," International Journal of Industrial Organization, Elsevier, vol. 82(C).
    4. Tomohiro Hayashida & Ichiro Nishizaki & Shinya Sekizaki & Junya Okabe, 2023. "Data Envelopment Analysis Approaches for Multiperiod Two-Level Production and Distribution Planning Problems," Mathematics, MDPI, vol. 11(21), pages 1-25, October.
    5. Gino Loyola, 2021. "Effects of competition in first-price auctions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(4), pages 1527-1567, June.

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    More about this item

    Keywords

    First-price auction; Commitment; Stackelberg game; Collusion; Subgame perfect equilibrium;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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