IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2110.08563.html
   My bibliography  Save this paper

Auction design with ambiguity: Optimality of the first-price and all-pay auctions

Author

Listed:
  • Sosung Baik
  • Sung-Ha Hwang

Abstract

We study the optimal auction design problem when bidders' preferences follow the maxmin expected utility model. We suppose that each bidder's set of priors consists of beliefs close to the seller's belief, where "closeness" is defined by a divergence. For a given allocation rule, we identify a class of optimal transfer candidates, named the win-lose dependent transfers, with the following property: each type of bidder's transfer conditional on winning or losing is independent of the competitor's type report. Our result reduces the infinite-dimensional optimal transfer problem to a two-dimensional optimization problem. By solving the reduced problem, we find that: (i) among efficient mechanisms with no premiums for losers, the first-price auction is optimal; and, (ii) among efficient winner-favored mechanisms where each bidder pays smaller amounts when she wins than loses: the all-pay auction is optimal. Under a simplifying assumption, these two auctions remain optimal under the endogenous allocation rule.

Suggested Citation

  • Sosung Baik & Sung-Ha Hwang, 2021. "Auction design with ambiguity: Optimality of the first-price and all-pay auctions," Papers 2110.08563, arXiv.org.
    • Handle: RePEc:arx:papers:2110.08563
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2110.08563
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sarah Auster & Christian Kellner, 2020. "Robust Bidding and Revenue in Descending Price Auctions," CRC TR 224 Discussion Paper Series crctr224_2020_146, University of Bonn and University of Mannheim, Germany.
    2. Yizhaq Minchuk & Aner Sela, 2020. "Contests with insurance," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 1-22, June.
    3. repec:bla:jindec:v:50:y:2002:i:4:p:417-30 is not listed on IDEAS
    4. Brunner, Christoph & Hu, Audrey & Oechssler, Jörg, 2014. "Premium auctions and risk preferences: An experimental study," Games and Economic Behavior, Elsevier, vol. 87(C), pages 467-484.
    5. Lars Peter Hansen & Thomas J Sargent, 2014. "Robust Control and Model Uncertainty," World Scientific Book Chapters, in: UNCERTAINTY WITHIN ECONOMIC MODELS, chapter 5, pages 145-154, World Scientific Publishing Co. Pte. Ltd..
    6. Milgrom,Paul, 2004. "Putting Auction Theory to Work," Cambridge Books, Cambridge University Press, number 9780521536721, November.
    7. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    8. Bos, Olivier, 2012. "Wars of attrition and all-pay auctions with stochastic competition," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 83-91.
    9. Auster, Sarah, 2018. "Robust contracting under common value uncertainty," Theoretical Economics, Econometric Society, vol. 13(1), January.
    10. Le Treust, Maël & Tomala, Tristan, 2019. "Persuasion with limited communication capacity," Journal of Economic Theory, Elsevier, vol. 184(C).
    11. Çağıl Koçyiğit & Garud Iyengar & Daniel Kuhn & Wolfram Wiesemann, 2020. "Distributionally Robust Mechanism Design," Management Science, INFORMS, vol. 66(1), pages 159-189, January.
    12. , & , & ,, 2006. "Optimal auctions with ambiguity," Theoretical Economics, Econometric Society, vol. 1(4), pages 411-438, December.
    13. Filip Matêjka & Alisdair McKay, 2015. "Rational Inattention to Discrete Choices: A New Foundation for the Multinomial Logit Model," American Economic Review, American Economic Association, vol. 105(1), pages 272-298, January.
    14. Bose, Subir & Daripa, Arup, 2009. "A dynamic mechanism and surplus extraction under ambiguity," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2084-2114, September.
    15. Laohakunakorn, Krittanai & Levy, Gilat & Razin, Ronny, 2019. "Private and common value auctions with ambiguity over correlation," Journal of Economic Theory, Elsevier, vol. 184(C).
    16. Chen Cohen & Todd R. Kaplan & Aner Sela, 2008. "Optimal rewards in contests," RAND Journal of Economics, RAND Corporation, vol. 39(2), pages 434-451, June.
    17. Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
    18. Ghosh, Gagan & Liu, Heng, 2021. "Sequential auctions with ambiguity," Journal of Economic Theory, Elsevier, vol. 197(C).
    19. Todd Kaplan & Israel Luski & Aner Sela & David Wettstein, 2002. "All–Pay Auctions with Variable Rewards," Journal of Industrial Economics, Wiley Blackwell, vol. 50(4), pages 417-430, December.
    20. Bodoh-Creed, Aaron L., 2012. "Ambiguous beliefs and mechanism design," Games and Economic Behavior, Elsevier, vol. 75(2), pages 518-537.
    21. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    22. Alexander Matros & Daniel Armanios, 2009. "Tullock’s contest with reimbursements," Public Choice, Springer, vol. 141(1), pages 49-63, October.
    23. Audrey Hu & Theo Offerman & Liang Zou, 2018. "How Risk Sharing may Enhance Efficiency of English Auctions," Economic Journal, Royal Economic Society, vol. 128(610), pages 1235-1256, May.
    24. Sims, Christopher A., 2003. "Implications of rational inattention," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 665-690, April.
    25. Jacob K. Goeree & Theo Offerman, 2004. "Notes and Comments the Amsterdam Auction," Econometrica, Econometric Society, vol. 72(1), pages 281-294, January.
    26. Krishna, Vijay & Morgan, John, 1997. "An Analysis of the War of Attrition and the All-Pay Auction," Journal of Economic Theory, Elsevier, vol. 72(2), pages 343-362, February.
    27. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    28. Kin Chung Lo, 1998. "Sealed bid auctions with uncertainty averse bidders," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(1), pages 1-20.
    29. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    30. Hu, Audrey & Offerman, Theo & Zou, Liang, 2011. "Premium auctions and risk preferences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2420-2439.
    31. Matthew Gentzkow & Emir Kamenica, 2014. "Costly Persuasion," American Economic Review, American Economic Association, vol. 104(5), pages 457-462, May.
    32. Laohakunakorn, Krittanai & Levy, Gilat & Razin, Ronny, 2019. "Private and common value auctions with ambiguity over correlation," LSE Research Online Documents on Economics 101410, London School of Economics and Political Science, LSE Library.
    33. Kocherlakota, Narayana R. & Song, Yangwei, 2019. "Public goods with ambiguity in large economies," Journal of Economic Theory, Elsevier, vol. 182(C), pages 218-246.
    34. Minchuk, Yizhaq, 2018. "Effect of reimbursement on all-pay auction," Economics Letters, Elsevier, vol. 172(C), pages 28-30.
    35. Wolitzky, Alexander, 2016. "Mechanism design with maxmin agents: theory and an application to bilateral trade," Theoretical Economics, Econometric Society, vol. 11(3), September.
    36. Steven Stong, 2018. "Ambiguity aversion in the all‐pay auction and war of attrition," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 20(6), pages 822-839, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sosung Baik & Sung-Ha Hwang, 2022. "Revenue Comparisons of Auctions with Ambiguity Averse Sellers," Papers 2211.12669, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sosung Baik & Sung-Ha Hwang, 2022. "Revenue Comparisons of Auctions with Ambiguity Averse Sellers," Papers 2211.12669, arXiv.org.
    2. Yizhaq Minchuk & Aner Sela, 2020. "Contests with insurance," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 1-22, June.
    3. Vasserman, Shoshana & Watt, Mitchell, 2021. "Risk aversion and auction design: Theoretical and empirical evidence," International Journal of Industrial Organization, Elsevier, vol. 79(C).
    4. Song, Yangwei, 2018. "Efficient Implementation with Interdependent Valuations and Maxmin Agents," Rationality and Competition Discussion Paper Series 92, CRC TRR 190 Rationality and Competition.
    5. Song, Yangwei, 2022. "Approximate Bayesian Implementation and Exact Maxmin Implementation: An Equivalence," Rationality and Competition Discussion Paper Series 362, CRC TRR 190 Rationality and Competition.
    6. Çağıl Koçyiğit & Garud Iyengar & Daniel Kuhn & Wolfram Wiesemann, 2020. "Distributionally Robust Mechanism Design," Management Science, INFORMS, vol. 66(1), pages 159-189, January.
    7. Evren, Özgür, 2019. "Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity," Games and Economic Behavior, Elsevier, vol. 114(C), pages 285-307.
    8. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    9. Song, Yangwei, 2023. "Approximate Bayesian implementation and exact maxmin implementation: An equivalence," Games and Economic Behavior, Elsevier, vol. 139(C), pages 56-87.
    10. Song, Yangwei, 2018. "Efficient implementation with interdependent valuations and maxmin agents," Journal of Economic Theory, Elsevier, vol. 176(C), pages 693-726.
    11. Takashi Ui, 2021. "Strategic Ambiguity in Global Games," Working Papers on Central Bank Communication 032, University of Tokyo, Graduate School of Economics.
    12. Sander Onderstal, 2020. "Premium auctions in the field," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 39-63, June.
    13. Auster, Sarah & Kellner, Christian, 2022. "Robust bidding and revenue in descending price auctions," Journal of Economic Theory, Elsevier, vol. 199(C).
    14. Takashi Ui, 2023. "Strategic Ambiguity in Global Games," Papers 2303.12263, arXiv.org, revised Nov 2024.
    15. Giuseppe Lopomo & Luca Rigotti & Chris Shannon, 2021. "Uncertainty in Mechanism Design," Papers 2108.12633, arXiv.org.
    16. Kocherlakota, Narayana R. & Song, Yangwei, 2019. "Public goods with ambiguity in large economies," Journal of Economic Theory, Elsevier, vol. 182(C), pages 218-246.
    17. Hu, Audrey & Offerman, Theo & Zou, Liang, 2011. "Premium auctions and risk preferences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2420-2439.
    18. Tang, Rui & Zhang, Mu, 2021. "Maxmin implementation," Journal of Economic Theory, Elsevier, vol. 194(C).
    19. Ellis, Andrew, 2018. "On dynamic consistency in ambiguous games," Games and Economic Behavior, Elsevier, vol. 111(C), pages 241-249.
    20. Guo, Huiyi, 2024. "Collusion-proof mechanisms for full surplus extraction," Games and Economic Behavior, Elsevier, vol. 145(C), pages 263-284.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2110.08563. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.