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On the Continuous Equilibria of Affiliated-Value, All-Pay Auctions with Private Budget Constraints, Third Version

Author

Listed:
  • Maciej H. Kotowski

    (John F. Kennedy School of Government, Harvard University)

  • Fei Li

    (Department of Economics University of North Carolina)

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.

Suggested Citation

  • Maciej H. Kotowski & Fei Li, 2012. "On the Continuous Equilibria of Affiliated-Value, All-Pay Auctions with Private Budget Constraints, Third Version," PIER Working Paper Archive 14-001, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 10 Jan 2014.
    • Handle: RePEc:pen:papers:14-001
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    References listed on IDEAS

    as
    1. Yeon-Koo Che & Ian Gale, 1998. "Standard Auctions with Financially Constrained Bidders," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(1), pages 1-21.
    2. Kotowski, Maciej H., 2020. "First-price auctions with budget constraints," Theoretical Economics, Econometric Society, vol. 15(1), January.
    3. Fang, Hanming & Parreiras, Sergio O., 2002. "Equilibrium of Affiliated Value Second Price Auctions with Financially Constrained Bidders: The Two-Bidder Case," Games and Economic Behavior, Elsevier, vol. 39(2), pages 215-236, May.
    4. , & ,, 2006. "Revenue comparisons for auctions when bidders have arbitrary types," Theoretical Economics, Econometric Society, vol. 1(1), pages 95-118, March.
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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. Kotowski, Maciej H., 2020. "First-price auctions with budget constraints," Theoretical Economics, Econometric Society, vol. 15(1), January.
    3. 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.
    4. Ghosh, Gagan & Liu, Heng, 2019. "Sequential second-price auctions with private budgets," Games and Economic Behavior, Elsevier, vol. 113(C), pages 611-632.
    5. 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.
    6. 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.
    7. Baisa, Brian & Rabinovich, Stanislav, 2016. "Optimal auctions with endogenous budgets," Economics Letters, Elsevier, vol. 141(C), pages 162-165.
    8. 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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