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On the continuous equilibria of affiliated-value, all-pay auctions with private budget constraints

Author

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  • Kotowski, Maciej H.
  • Li, Fei
Abstract
We consider all-pay auctions in the presence of interdependent, affiliated valuations and private budget constraints. For the sealed-bid, all-pay auction we characterize a symmetric equilibrium in continuous strategies for the case of N bidders. Budget constraints encourage more aggressive bidding among participants with large endowments and intermediate valuations. We extend our results to the war of attrition where we show that budget constraints lead to a uniform amplification of equilibrium bids among bidders with sufficient endowments. An example shows that with both interdependent valuations and private budget constraints, a revenue ranking between the two auction formats is generally not possible. Equilibria with discontinuous bidding strategies are discussed.

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  • Kotowski, Maciej H. & Li, Fei, 2014. "On the continuous equilibria of affiliated-value, all-pay auctions with private budget constraints," Games and Economic Behavior, Elsevier, vol. 85(C), pages 84-108.
    • Handle: RePEc:eee:gamebe:v:85:y:2014:i:c:p:84-108
    DOI: 10.1016/j.geb.2014.01.014
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    Cited by:

    1. Bobkova, Nina, 2020. "Asymmetric budget constraints in a first-price auction," Journal of Economic Theory, Elsevier, vol. 186(C).
    2. Ghosh, Gagan & Liu, Heng, 2019. "Sequential second-price auctions with private budgets," Games and Economic Behavior, Elsevier, vol. 113(C), pages 611-632.
    3. Kotowski, Maciej H. & Li, Fei, 2014. "On the continuous equilibria of affiliated-value, all-pay auctions with private budget constraints," Games and Economic Behavior, Elsevier, vol. 85(C), pages 84-108.
    4. Kotowski, Maciej H. & Li, Fei, 2014. "The war of attrition and the revelation of valuable information," Economics Letters, Elsevier, vol. 124(3), pages 420-423.
    5. Kotowski, Maciej H., 2020. "First-price auctions with budget constraints," Theoretical Economics, Econometric Society, vol. 15(1), January.
    6. 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.
    7. Ulrich Bergmann & Arkady Konovalov, 2024. "Auction design and order of sale with budget-constrained bidders," Experimental Economics, Springer;Economic Science Association, vol. 27(1), pages 36-57, March.
    8. Baisa, Brian & Rabinovich, Stanislav, 2016. "Optimal auctions with endogenous budgets," Economics Letters, Elsevier, vol. 141(C), pages 162-165.
    9. Ghosh, Gagan, 2021. "Simultaneous auctions with budgets: Equilibrium existence and characterization," Games and Economic Behavior, Elsevier, vol. 126(C), pages 75-93.
    10. Jianfu Shen & Frederik Pretorius & K. W. Chau, 2018. "Land Auctions with Budget Constraints," The Journal of Real Estate Finance and Economics, Springer, vol. 56(3), pages 443-471, April.

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    More about this item

    Keywords

    All-pay auction; War of attrition; Budget constraints; Common values; Private values; Affiliation; Contests;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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