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Asymmetric budget constraints in a first-price auction

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  • Bobkova, Nina

Abstract

I solve a first-price auction for two bidders with asymmetric budget distributions and known valuations for one object. I show that in any equilibrium, the expected utilities and bid distributions of both bidders are unique. If budgets are sufficiently low, the bidders will bid their entire budget in any equilibrium. For sufficiently high budgets, mass points in the equilibrium strategies arise. A less restrictive budget distribution could make both bidders strictly worse off. If the budget distribution of one bidder is dominated by the budget distribution of the other bidder in the reverse-hazard-rate order, the weaker bidder will bid more aggressively than the stronger bidder. In contrast to existing results for symmetric budget distributions, with asymmetric budget distributions, a second-price auction can yield a strictly higher revenue than a first-price auction. Under an additional assumption, I derive the unique equilibrium utilities and bid distributions of both bidders in an all-pay auction.

Suggested Citation

  • Bobkova, Nina, 2020. "Asymmetric budget constraints in a first-price auction," Journal of Economic Theory, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:jetheo:v:186:y:2020:i:c:s0022053119301231
    DOI: 10.1016/j.jet.2019.104975
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    Cited by:

    1. Boulatov, Alexei & Severinov, Sergei, 2021. "Optimal and efficient mechanisms with asymmetrically budget constrained buyers," Games and Economic Behavior, Elsevier, vol. 127(C), pages 155-178.
    2. Kotowski, Maciej H., 2020. "First-price auctions with budget constraints," Theoretical Economics, Econometric Society, vol. 15(1), January.
    3. Zhonghao Shui, 2023. "Rejection prices and an auctioneer with non-monotonic utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 925-951, September.
    4. Bingchao Huangfu & Gagan Ghosh & Heng Liu, 2023. "Resource inequality in the war of attrition," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 33-61, March.
    5. Kariv, Shachar & Kotowski, Maciej H. & Leister, C. Matthew, 2018. "Liquidity risk in sequential trading networks," Games and Economic Behavior, Elsevier, vol. 109(C), pages 565-581.
    6. 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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    More about this item

    Keywords

    Budget constraints; Asymmetric bidders; First-price auctions; All-pay auctions;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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