IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i3p403-d735941.html
   My bibliography  Save this article

The Generalized First- and Second-Price Auctions: Overbidding, Underbidding, and Optimal Reserve Price

Author

Listed:
  • Ziyi Tan

    (Department of Quantitative Economics, University of International Business and Economics, Beijing 100029, China)

  • Shulin Liu

    (Department of Quantitative Economics, University of International Business and Economics, Beijing 100029, China)

Abstract

The paper generalizes the models of the standard first- and second-price auctions (FPA and SPA) by using the Cobb-Douglas function to evaluate bidders’ two conflicting bidding preferences for the probability of winning the item ( C pwin ) and the profit conditional on winning ( C profit ). Compared with the popular expected profit function, this function has the advantage of allowing the bidders to equally or differently value C pwin and C profit from the point of view of multiple criteria decision making, and then can capture bidders’ bidding behavior in reality. Introduction of the Cobb-Douglas function into the FPA allows us to provide new interpretations for overbidding (underbidding) behavior and the dependence of the optimal reserve price on the number of bidders. Our new interpretations are all attributed to the bidders’ different preferences for C pwin and C profit . In contrast, this introduction into the SPA does not matter. Our findings suggest that the seller should prefer the FPA (SPA) over the SPA (FPA) and set a lower (higher) optimal reserve price if he conjectures that the bidders have a stronger desire to win an auction (to obtain a profit). The above results help the seller to select between the two auctions and set a reserve price in practice.

Suggested Citation

  • Ziyi Tan & Shulin Liu, 2022. "The Generalized First- and Second-Price Auctions: Overbidding, Underbidding, and Optimal Reserve Price," Mathematics, MDPI, vol. 10(3), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:403-:d:735941
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/3/403/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/3/403/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Liu, Shulin & Wang, Mingxi, 2010. "Sealed-bid auctions based on Cobb-Douglas utility function," Economics Letters, Elsevier, vol. 107(1), pages 1-3, April.
    2. Ghatak, Maitreesh & Nien-Huei Jiang, Neville, 2002. "A simple model of inequality, occupational choice, and development," Journal of Development Economics, Elsevier, vol. 69(1), pages 205-226, October.
    3. Ivanova-Stenzel, Radosveta & Sonsino, Doron, 2004. "Comparative study of one-bid versus two-bid auctions," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 561-583, August.
    4. Stephanie Rosenkranz & Patrick W. Schmitz, 2007. "Reserve Prices in Auctions as Reference Points," Economic Journal, Royal Economic Society, vol. 117(520), pages 637-653, April.
    5. Kerim Keskin, 2016. "Inverse S-shaped probability weighting functions in first-price sealed-bid auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 20(1), pages 57-67, March.
    6. Audrey Hu & Steven A. Matthews & Liang Zou, 2009. "Risk Aversion and Optimal Reserve Prices in First and Second-Price Auctions, Second Version," PIER Working Paper Archive 10-001, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 03 Jan 2010.
    7. Oliver Kirchkamp & J. Philipp Reiß, 2019. "Heterogeneous bids in auctions with rational and boundedly rational bidders: theory and experiment," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(4), pages 1001-1031, December.
    8. Armantier, Olivier & Treich, Nicolas, 2009. "Star-shaped probability weighting functions and overbidding in first-price auctions," Economics Letters, Elsevier, vol. 104(2), pages 83-85, August.
    9. Salo, Ahti A & Weber, Martin, 1995. "Ambiguity Aversion in First-Price Sealed-Bid Auctions," Journal of Risk and Uncertainty, Springer, vol. 11(2), pages 123-137, September.
    10. Riley, John G & Samuelson, William F, 1981. "Optimal Auctions," American Economic Review, American Economic Association, vol. 71(3), pages 381-392, June.
    11. Tsai, Jeng-Yan, 2013. "Bank interest margin management based on a path-dependent Cobb–Douglas utility framework," Economic Modelling, Elsevier, vol. 35(C), pages 751-762.
    12. Andreas Roider & Patrick W. Schmitz, 2012. "Auctions with Anticipated Emotions: Overbidding, Underbidding, and Optimal Reserve Prices," Scandinavian Journal of Economics, Wiley Blackwell, vol. 114(3), pages 808-830, September.
    13. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    14. Lange, Andreas & Ratan, Anmol, 2010. "Multi-dimensional reference-dependent preferences in sealed-bid auctions - How (most) laboratory experiments differ from the field," Games and Economic Behavior, Elsevier, vol. 68(2), pages 634-645, March.
    15. Ahmad, Husnain Fateh, 2015. "Endogenous price expectations as reference points in auctions," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 46-63.
    16. Cox, James C. & Smith, Vernon L. & Walker, James M., 1983. "Tests of a heterogeneous bidders theory of first price auctions," Economics Letters, Elsevier, vol. 12(3-4), pages 207-212.
    17. Kerim Keskin, 2016. "Inverse S-shaped probability weighting functions in first-price sealed-bid auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 20(1), pages 57-67, March.
    18. Kagel, John H & Roth, Alvin E, 1992. "Theory and Misbehavior in First-Price Auctions: Comment," American Economic Review, American Economic Association, vol. 82(5), pages 1379-1391, December.
    19. Li, Yanhai, 2020. "Optimal reserve prices in sealed-bid auctions with reference effects," International Journal of Industrial Organization, Elsevier, vol. 71(C).
    20. Cox, James C & Smith, Vernon L & Walker, James M, 1988. "Theory and Individual Behavior of First-Price Auctions," Journal of Risk and Uncertainty, Springer, vol. 1(1), pages 61-99, March.
    21. Hu, Audrey & Matthews, Steven A. & Zou, Liang, 2010. "Risk aversion and optimal reserve prices in first- and second-price auctions," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1188-1202, May.
    22. Emel Filiz-Ozbay & Erkut Y. Ozbay, 2007. "Auctions with Anticipated Regret: Theory and Experiment," American Economic Review, American Economic Association, vol. 97(4), pages 1407-1418, September.
    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. Antonio C. C. Perrelli & Eduardo A. Sodré & André V. R. N. Silva & Caarem D. S. Studzinski & Vinícius F. Silva & Dalton F. G. Filho & Armando T. Neto & Alex A. B. Santos, 2024. "Optimizing Price Markup: The Impact of Power Purchase Agreements and Energy Production Uncertainty on the Economic Performance of Onshore and Offshore Wind Farms," International Journal of Energy Economics and Policy, Econjournals, vol. 14(5), pages 211-219, September.

    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. Andreas Roider & Patrick W. Schmitz, 2012. "Auctions with Anticipated Emotions: Overbidding, Underbidding, and Optimal Reserve Prices," Scandinavian Journal of Economics, Wiley Blackwell, vol. 114(3), pages 808-830, September.
    2. Li, Yanhai, 2020. "Optimal reserve prices in sealed-bid auctions with reference effects," International Journal of Industrial Organization, Elsevier, vol. 71(C).
    3. Ahmad, Husnain Fateh, 2015. "Endogenous price expectations as reference points in auctions," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 46-63.
    4. Zeynep Kantur & Kerim Keskin, 2019. "On (mis-)perception of probabilities in first-price sealed-bid auctions," Economics Bulletin, AccessEcon, vol. 39(1), pages 726-733.
    5. Kerim Keskin, 2016. "Inverse S-shaped probability weighting functions in first-price sealed-bid auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 20(1), pages 57-67, March.
    6. Vasserman, Shoshana & Watt, Mitchell, 2021. "Risk aversion and auction design: Theoretical and empirical evidence," International Journal of Industrial Organization, Elsevier, vol. 79(C).
    7. Kim, Dong-Hyuk & Ratan, Anmol, 2022. "Disentangling risk aversion and loss aversion in first-price auctions: An empirical approach," European Economic Review, Elsevier, vol. 150(C).
    8. Kerim Keskin, 2016. "Inverse S-shaped probability weighting functions in first-price sealed-bid auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 20(1), pages 57-67, March.
    9. Bartling, Björn & Netzer, Nick, 2016. "An externality-robust auction: Theory and experimental evidence," Games and Economic Behavior, Elsevier, vol. 97(C), pages 186-204.
    10. Zhang, Yunyi & Gong, Pu, 2018. "IPV model with Cobb–Douglas and reference-dependent utility functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 121-131.
    11. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    12. Zhe Chen, 2021. "The multidimensional procurement auctions with reference‐based utility," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(2), pages 319-325, March.
    13. Josheski Dushko & Apostolov Mico, 2023. "The Prospect Theory and First Price Auctions: an Explanation of Overbidding," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 27(1), pages 33-74, March.
    14. Sascha Füllbrunn & Dirk‐Jan Janssen & Utz Weitzel, 2019. "Risk Aversion And Overbidding In First Price Sealed Bid Auctions: New Experimental Evidence," Economic Inquiry, Western Economic Association International, vol. 57(1), pages 631-647, January.
    15. Hu, Audrey & Offerman, Theo & Zou, Liang, 2011. "Premium auctions and risk preferences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2420-2439.
    16. Kathryn Graddy & Lara Loewenstein & Jianping Mei & Mike Moses & Rachel A. J. Pownall, 2023. "Empirical evidence of anchoring and loss aversion from art auctions," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 47(2), pages 279-301, June.
    17. Grundl, Serafin & Zhu, Yu, 2019. "Identification and estimation of risk aversion in first-price auctions with unobserved auction heterogeneity," Journal of Econometrics, Elsevier, vol. 210(2), pages 363-378.
    18. Roman M. Sheremeta, 2016. "Impulsive Behavior in Competition: Testing Theories of Overbidding in Rent-Seeking Contests," Working Papers 16-21, Chapman University, Economic Science Institute.
    19. Hu, Audrey, 2011. "How bidder's number affects optimal reserve price in first-price auctions under risk aversion," Economics Letters, Elsevier, vol. 113(1), pages 29-31, October.
    20. Eisenhuth, Roland, 2010. "Auction Design with Loss Averse Bidders: The Optimality of All Pay Mechanisms," MPRA Paper 23357, University Library of Munich, Germany.

    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:gam:jmathe:v:10:y:2022:i:3:p:403-:d:735941. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.