IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2202.07517.html
   My bibliography  Save this paper

An Equilibrium Model of the First-Price Auction with Strategic Uncertainty: Theory and Empirics

Author

Listed:
  • Bernhard Kasberger

Abstract

In many first-price auctions, bidders face considerable strategic uncertainty: They cannot perfectly anticipate the other bidders' bidding behavior. We propose a model in which bidders do not know the entire distribution of opponent bids but only the expected (winning) bid and lower and upper bounds on the opponent bids. We characterize the optimal bidding strategies and prove the existence of equilibrium beliefs. Finally, we apply the model to estimate the cost distribution in highway procurement auctions and find good performance out-of-sample.

Suggested Citation

  • Bernhard Kasberger, 2022. "An Equilibrium Model of the First-Price Auction with Strategic Uncertainty: Theory and Empirics," Papers 2202.07517, arXiv.org, revised Mar 2022.
    • Handle: RePEc:arx:papers:2202.07517
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2202.07517
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Emmanuel Guerre & Isabelle Perrigne & Quang Vuong, 2000. "Optimal Nonparametric Estimation of First-Price Auctions," Econometrica, Econometric Society, vol. 68(3), pages 525-574, May.
    2. Lo, Kin Chung, 1996. "Equilibrium in Beliefs under Uncertainty," Journal of Economic Theory, Elsevier, vol. 71(2), pages 443-484, November.
    3. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    4. Mariann Ollár & Antonio Penta, 2017. "Full Implementation and Belief Restrictions," American Economic Review, American Economic Association, vol. 107(8), pages 2243-2277, August.
    5. Tim Roughgarden, 2020. "Transaction Fee Mechanism Design for the Ethereum Blockchain: An Economic Analysis of EIP-1559," Papers 2012.00854, arXiv.org.
    6. Ioana Popescu, 2005. "A Semidefinite Programming Approach to Optimal-Moment Bounds for Convex Classes of Distributions," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 632-657, August.
    7. Renou, Ludovic & Schlag, Karl H., 2010. "Minimax regret and strategic uncertainty," Journal of Economic Theory, Elsevier, vol. 145(1), pages 264-286, January.
    8. Pierpaolo Battigalli & Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci, 2015. "Self-Confirming Equilibrium and Model Uncertainty," American Economic Review, American Economic Association, vol. 105(2), pages 646-677, February.
    9. James E. Smith, 1995. "Generalized Chebychev Inequalities: Theory and Applications in Decision Analysis," Operations Research, INFORMS, vol. 43(5), pages 807-825, October.
    10. Elodie Guerre & I. Perrigne & Q.H. Vuong, 2000. "Optimal nonparametric estimation of first-price auctions [[Estimation nonparamétrique optimale des enchères au premier prix]]," Post-Print hal-02697497, HAL.
    11. Philip A. Haile & Han Hong & Matthew Shum, 2003. "Nonparametric Tests for Common Values in First-Price Sealed-Bid Auctions," Cowles Foundation Discussion Papers 1445, Cowles Foundation for Research in Economics, Yale University.
    12. Ehud Lehrer, 2012. "Partially Specified Probabilities: Decisions and Games," American Economic Journal: Microeconomics, American Economic Association, vol. 4(1), pages 70-100, February.
    13. Hayashi, Takashi, 2008. "Regret aversion and opportunity dependence," Journal of Economic Theory, Elsevier, vol. 139(1), pages 242-268, March.
    14. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    15. Chen, Yan & Katuscak, Peter & Ozdenoren, Emre, 2007. "Sealed bid auctions with ambiguity: Theory and experiments," Journal of Economic Theory, Elsevier, vol. 136(1), pages 513-535, September.
    16. Battigalli, P. & Cerreia-Vioglio, S. & Maccheroni, F. & Marinacci, M., 2016. "Analysis of information feedback and selfconfirming equilibrium," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 40-51.
    17. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    18. Athey, Susan & Haile, Philip A., 2007. "Nonparametric Approaches to Auctions," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 60, Elsevier.
    19. Carrasco, Vinicius & Farinha Luz, Vitor & Kos, Nenad & Messner, Matthias & Monteiro, Paulo & Moreira, Humberto, 2018. "Optimal selling mechanisms under moment conditions," Journal of Economic Theory, Elsevier, vol. 177(C), pages 245-279.
    20. Eichberger, Jurgen & Kelsey, David, 2000. "Non-Additive Beliefs and Strategic Equilibria," Games and Economic Behavior, Elsevier, vol. 30(2), pages 183-215, February.
    21. Dow James & Werlang Sergio Ribeiro Da Costa, 1994. "Nash Equilibrium under Knightian Uncertainty: Breaking Down Backward Induction," Journal of Economic Theory, Elsevier, vol. 64(2), pages 305-324, December.
    22. Elena Krasnokutskaya, 2011. "Identification and Estimation of Auction Models with Unobserved Heterogeneity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(1), pages 293-327.
    23. Georgia Perakis & Guillaume Roels, 2008. "Regret in the Newsvendor Model with Partial Information," Operations Research, INFORMS, vol. 56(1), pages 188-203, February.
    24. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    25. 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.
    26. Patrick Bajari & Stephanie Houghton & Steven Tadelis, 2014. "Bidding for Incomplete Contracts: An Empirical Analysis of Adaptation Costs," American Economic Review, American Economic Association, vol. 104(4), pages 1288-1319, April.
    27. Matt Shum & Phil Haile & Han Hong, 2003. "Nonparametric Tests for Common Values in First-Price Auctions," Economics Working Paper Archive 501, The Johns Hopkins University,Department of Economics.
    28. Gerhard Winkler, 1988. "Extreme Points of Moment Sets," Mathematics of Operations Research, INFORMS, vol. 13(4), pages 581-587, November.
    29. Linhart, P. B. & Radner, R., 1989. "Minimax-regret strategies for bargaining over several variables," Journal of Economic Theory, Elsevier, vol. 48(1), pages 152-178, June.
    30. Yingni Guo & Eran Shmaya, 2019. "Robust Monopoly Regulation," Papers 1910.04260, arXiv.org.
    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. Kasberger, Bernhard & Woodward, Kyle, 2021. "Bidding in Multi-Unit Auctions under Limited Information," MPRA Paper 111185, University Library of Munich, Germany.

    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. Galeazzi, Paolo & Marti, Johannes, 2023. "Choice structures in games," Games and Economic Behavior, Elsevier, vol. 140(C), pages 431-455.
    2. Ronald Stauber, 2019. "A strategic product for belief functions," ANU Working Papers in Economics and Econometrics 2019-668, Australian National University, College of Business and Economics, School of Economics.
    3. Frank Riedel & Linda Sass, 2014. "Ellsberg games," Theory and Decision, Springer, vol. 76(4), pages 469-509, April.
    4. Kasberger, Bernhard & Woodward, Kyle, 2021. "Bidding in Multi-Unit Auctions under Limited Information," MPRA Paper 111185, University Library of Munich, Germany.
    5. Atsushi Kajii & Takashi Ui, 2005. "Incomplete Information Games With Multiple Priors," The Japanese Economic Review, Japanese Economic Association, vol. 56(3), pages 332-351, September.
    6. Stauber, Ronald, 2019. "A strategic product for belief functions," Games and Economic Behavior, Elsevier, vol. 116(C), pages 38-64.
    7. Renou, Ludovic & Schlag, Karl H., 2010. "Minimax regret and strategic uncertainty," Journal of Economic Theory, Elsevier, vol. 145(1), pages 264-286, January.
    8. Marmer, Vadim & Shneyerov, Artyom, 2012. "Quantile-based nonparametric inference for first-price auctions," Journal of Econometrics, Elsevier, vol. 167(2), pages 345-357.
    9. 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.
    10. Lang, Matthias & Wambach, Achim, 2013. "The fog of fraud – Mitigating fraud by strategic ambiguity," Games and Economic Behavior, Elsevier, vol. 81(C), pages 255-275.
    11. Stauber, Ronald, 2017. "Irrationality and ambiguity in extensive games," Games and Economic Behavior, Elsevier, vol. 102(C), pages 409-432.
    12. Yang, Jian, 2018. "Game-theoretic modeling of players’ ambiguities on external factors," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 31-56.
    13. Ma, Jun & Marmer, Vadim & Shneyerov, Artyom, 2019. "Inference for first-price auctions with Guerre, Perrigne, and Vuong’s estimator," Journal of Econometrics, Elsevier, vol. 211(2), pages 507-538.
    14. Nathalie Gimenes & Emmanuel Guerre, 2019. "Nonparametric identification of an interdependent value model with buyer covariates from first-price auction bids," Papers 1910.10646, arXiv.org.
    15. Ghosh, Gagan & Liu, Heng, 2021. "Sequential auctions with ambiguity," Journal of Economic Theory, Elsevier, vol. 197(C).
    16. Jun Ma & Vadim Marmer & Artyom Shneyerov & Pai Xu, 2021. "Monotonicity-constrained nonparametric estimation and inference for first-price auctions," Econometric Reviews, Taylor & Francis Journals, vol. 40(10), pages 944-982, November.
    17. Hema Yoganarasimhan, 2016. "Estimation of Beauty Contest Auctions," Marketing Science, INFORMS, vol. 35(1), pages 27-54, January.
    18. Hickman Brent R. & Hubbard Timothy P. & Sağlam Yiğit, 2012. "Structural Econometric Methods in Auctions: A Guide to the Literature," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 67-106, August.
    19. Mass, Helene, 2018. "Strategies under strategic uncertainty," ZEW Discussion Papers 18-055, ZEW - Leibniz Centre for European Economic Research.
    20. Hickman Brent R. & Hubbard Timothy P. & Sağlam Yiğit, 2012. "Structural Econometric Methods in Auctions: A Guide to the Literature," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 67-106, August.

    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:2202.07517. 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.