IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v82y2013icp350-368.html
   My bibliography  Save this article

Bilateral k+1-price auctions with asymmetric shares and values

Author

Listed:
  • Wasser, Cédric

Abstract

We study a sealed-bid auction between two bidders with asymmetric independent private values. The two bidders own asymmetric shares in a partnership. The higher bidder buys the lower bidderʼs shares at a per-unit price that is a convex combination of the two bids. The weight of the lower bid is denoted by k∈[0,1]. We partially characterize equilibrium strategies and show that they are closely related to equilibrium strategies of two well-studied mechanisms: the double auction between a buyer and a seller and the first-price auction between two buyers (or two sellers). Combining results from those two branches of the literature enables us to prove equilibrium existence. Moreover, we find that there is a continuum of equilibria if k∈(0,1) whereas the equilibrium is unique if k∈{0,1}. Our approach also suggests a procedure for numerical simulations.

Suggested Citation

  • Wasser, Cédric, 2013. "Bilateral k+1-price auctions with asymmetric shares and values," Games and Economic Behavior, Elsevier, vol. 82(C), pages 350-368.
    • Handle: RePEc:eee:gamebe:v:82:y:2013:i:c:p:350-368
    DOI: 10.1016/j.geb.2013.07.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825613001176
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2013.07.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Athanassoglou, Stergios & Brams, Steven J. & Sethuraman, Jay, 2010. "A note on the inefficiency of bidding over the price of a share," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 191-195, November.
    2. Marshall Robert C. & Meurer Michael J. & Richard Jean-Francois & Stromquist Walter, 1994. "Numerical Analysis of Asymmetric First Price Auctions," Games and Economic Behavior, Elsevier, vol. 7(2), pages 193-220, September.
    3. de Frutos, M. Angeles, 2000. "Asymmetric Price-Benefits Auctions," Games and Economic Behavior, Elsevier, vol. 33(1), pages 48-71, October.
    4. Burkart, Mike, 1995. "Initial Shareholdings and Overbidding in Takeover Contests," Journal of Finance, American Finance Association, vol. 50(5), pages 1491-1515, December.
    5. María‐Angeles de Frutos & Thomas Kittsteiner, 2008. "Efficient partnership dissolution under buy‐sell clauses," RAND Journal of Economics, RAND Corporation, vol. 39(1), pages 184-198, March.
    6. Jeremy Bulow & Ming Huang & Paul Klemperer, 1999. "Toeholds and Takeovers," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 427-454, June.
    7. Kittsteiner, Thomas, 2003. "Partnerships and double auctions with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 44(1), pages 54-76, July.
    8. Stefano Galavotti & Nozomu Muto & Daisuke Oyama, 2011. "On efficient partnership dissolution under ex post individual rationality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(1), pages 87-123, September.
    9. Eric Maskin & John Riley, 2000. "Asymmetric Auctions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 413-438.
    10. Emiel Maasland & Sander Onderstal, 2007. "Auctions with Financial Externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(3), pages 551-574, September.
    11. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    12. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April.
    13. Fieseler, Karsten & Kittsteiner, Thomas & Moldovanu, Benny, 2003. "Partnerships, lemons, and efficient trade," Journal of Economic Theory, Elsevier, vol. 113(2), pages 223-234, December.
    14. Cramton, Peter & Gibbons, Robert & Klemperer, Paul, 1987. "Dissolving a Partnership Efficiently," Econometrica, Econometric Society, vol. 55(3), pages 615-632, May.
    15. Lu, Jingfeng, 2012. "Optimal auctions with asymmetric financial externalities," Games and Economic Behavior, Elsevier, vol. 74(2), pages 561-575.
    16. Chillemi, Ottorino, 2005. "Cross-owned firms competing in auctions," Games and Economic Behavior, Elsevier, vol. 51(1), pages 1-19, April.
    17. Fibich, Gadi & Gavish, Nir, 2011. "Numerical simulations of asymmetric first-price auctions," Games and Economic Behavior, Elsevier, vol. 73(2), pages 479-495.
    18. Olivier Bos, 2020. "Charitable asymmetric bidders," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(2), pages 320-337, April.
    19. Kalyan Chatterjee & William Samuelson, 1983. "Bargaining under Incomplete Information," Operations Research, INFORMS, vol. 31(5), pages 835-851, October.
    20. Lebrun, Bernard, 2006. "Uniqueness of the equilibrium in first-price auctions," Games and Economic Behavior, Elsevier, vol. 55(1), pages 131-151, April.
    21. Satterthwaite, Mark A. & Williams, Steven R., 1989. "Bilateral trade with the sealed bid k-double auction: Existence and efficiency," Journal of Economic Theory, Elsevier, vol. 48(1), pages 107-133, June.
    22. Maxim Engers & Brian McManus, 2007. "Charity Auctions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(3), pages 953-994, August.
    23. Preston McAfee, R., 1992. "Amicable divorce: Dissolving a partnership with simple mechanisms," Journal of Economic Theory, Elsevier, vol. 56(2), pages 266-293, April.
    24. Lebrun, Bernard, 1999. "First Price Auctions in the Asymmetric N Bidder Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(1), pages 125-142, February.
    25. Engelbrecht-Wiggans Richard, 1994. "Auctions with Price-Proportional Benefits to Bidders," Games and Economic Behavior, Elsevier, vol. 6(3), pages 339-346, May.
    26. Sudipto Dasgupta & Kevin Tsui, 2004. "Auctions with cross-shareholdings," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 163-194, July.
    27. Leininger, W. & Linhart, P. B. & Radner, R., 1989. "Equilibria of the sealed-bid mechanism for bargaining with incomplete information," Journal of Economic Theory, Elsevier, vol. 48(1), pages 63-106, June.
    28. Jacob K. Goeree & Emiel Maasland & Sander Onderstal & John L. Turner, 2005. "How (Not) to Raise Money," Journal of Political Economy, University of Chicago Press, vol. 113(4), pages 897-926, August.
    29. Williams, Steven R., 1987. "Efficient performance in two agent bargaining," Journal of Economic Theory, Elsevier, vol. 41(1), pages 154-172, February.
    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. Bernard Lebrun, 2015. "Revenue-superior variants of the second-price auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 245-275, June.
    2. Loertscher, Simon & Wasser, Cédric, 2019. "Optimal structure and dissolution of partnerships," Theoretical Economics, Econometric Society, vol. 14(3), July.
    3. Matt Van Essen & John Wooders, 2023. "Dual auctions for assigning winners and compensating losers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1069-1114, November.

    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. Kittsteiner, Thomas, 2003. "Partnerships and double auctions with interdependent valuations," Games and Economic Behavior, Elsevier, vol. 44(1), pages 54-76, July.
    2. Athanassoglou, Stergios & Brams, Steven J. & Sethuraman, Jay, 2010. "A note on the inefficiency of bidding over the price of a share," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 191-195, November.
    3. Bartling, Björn & Netzer, Nick, 2016. "An externality-robust auction: Theory and experimental evidence," Games and Economic Behavior, Elsevier, vol. 97(C), pages 186-204.
    4. de Frutos, M. Angeles, 2000. "Asymmetric Price-Benefits Auctions," Games and Economic Behavior, Elsevier, vol. 33(1), pages 48-71, October.
    5. Jehiel, Philippe & Moldovanu, Benny, 2005. "Allocative and Informational Externalities in Auctions and Related Mechanisms," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 142, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    6. María‐Angeles de Frutos & Thomas Kittsteiner, 2008. "Efficient partnership dissolution under buy‐sell clauses," RAND Journal of Economics, RAND Corporation, vol. 39(1), pages 184-198, March.
    7. Blumrosen, Liad & Dobzinski, Shahar, 2021. "(Almost) efficient mechanisms for bilateral trading," Games and Economic Behavior, Elsevier, vol. 130(C), pages 369-383.
    8. Lu, Jingfeng, 2012. "Optimal auctions with asymmetric financial externalities," Games and Economic Behavior, Elsevier, vol. 74(2), pages 561-575.
    9. Björn Bartling & Tobias Gesche & Nick Netzer, 2017. "Does the absence of human sellers bias bidding behavior in auction experiments?," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 3(1), pages 44-61, July.
    10. Ludwig Ensthaler & Thomas Giebe & Jianpei Li, 2014. "Speculative partnership dissolution with auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 18(2), pages 127-150, June.
    11. Bernard Lebrun, 2015. "Revenue-superior variants of the second-price auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 245-275, June.
    12. Dodonova, Anna & Khoroshilov, Yuri, 2014. "Can preemptive bidding in takeover auctions be socially optimal? Yes it can," The North American Journal of Economics and Finance, Elsevier, vol. 27(C), pages 34-47.
    13. Jianpei Li & Yi Xue & Weixing Wu, 2013. "Partnership dissolution and proprietary information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(2), pages 495-527, February.
    14. repec:dau:papers:123456789/5431 is not listed on IDEAS
    15. Timothy Hubbard & René Kirkegaard & Harry Paarsch, 2013. "Using Economic Theory to Guide Numerical Analysis: Solving for Equilibria in Models of Asymmetric First-Price Auctions," Computational Economics, Springer;Society for Computational Economics, vol. 42(2), pages 241-266, August.
    16. Lorentziadis, Panos L., 2016. "Optimal bidding in auctions from a game theory perspective," European Journal of Operational Research, Elsevier, vol. 248(2), pages 347-371.
    17. Lu, Hu & Robert, Jacques, 2001. "Optimal Trading Mechanisms with Ex Ante Unidentified Traders," Journal of Economic Theory, Elsevier, vol. 97(1), pages 50-80, March.
    18. John Turner, 2013. "Dissolving (in)effective partnerships," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 321-335, July.
    19. Gino Loyola, 2021. "Optimal selling mechanisms with crossholdings," Review of Economic Design, Springer;Society for Economic Design, vol. 25(1), pages 1-32, June.
    20. Ornelas, Emanuel & Turner, John L., 2007. "Efficient dissolution of partnerships and the structure of control," Games and Economic Behavior, Elsevier, vol. 60(1), pages 187-199, July.
    21. Li, Jianpei, 2009. "Partnership Dissolution and Proprietary Information," MPRA Paper 12505, University Library of Munich, Germany.

    More about this item

    Keywords

    Asymmetric auctions; Double auction; First-price auction; Partnership dissolution; Detail-free mechanism;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    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:eee:gamebe:v:82:y:2013:i:c:p:350-368. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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.