IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v108y2018icp170-181.html
   My bibliography  Save this article

Shapley value based pricing for auctions and exchanges

Author

Listed:
  • Lindsay, Luke

Abstract

This paper explores how the Shapley value can be used as the basis of a payment rule for auctions and exchanges. The standard Shapley value is modified so that losing bidders do not make or receive any payments. The new rule, called the balanced winner contribution (BWC) rule, satisfies a variation of Myerson's balanced contribution property. The payment rule is fair in the sense that, with respect to reported values, the members of every pair of traders make equal contributions to each other's share of the gains from trade. BWC payments can be used in single-item auctions and more complex auctions and exchanges with multiple items and package bidding. A series of examples is presented to illustrate how the BWC rule works and how the payments compare to those based on competitive prices, the core, and the Vickrey–Clarke–Groves mechanism.

Suggested Citation

  • Lindsay, Luke, 2018. "Shapley value based pricing for auctions and exchanges," Games and Economic Behavior, Elsevier, vol. 108(C), pages 170-181.
  • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:170-181
    DOI: 10.1016/j.geb.2017.10.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825617301926
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.geb.2017.10.020?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. Bykowsky, Mark M & Cull, Robert J & Ledyard, John O, 2000. "Mutually Destructive Bidding: The FCC Auction Design Problem," Journal of Regulatory Economics, Springer, vol. 17(3), pages 205-228, May.
    2. Aytek Erdil & Paul Klemperer, 2010. "A New Payment Rule for Core-Selecting Package Auctions," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 537-547, 04-05.
    3. B. Douglas Bernheim & Michael D. Whinston, 1986. "Menu Auctions, Resource Allocation, and Economic Influence," The Quarterly Journal of Economics, Oxford University Press, vol. 101(1), pages 1-31.
    4. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    5. Telser, Lester G, 1996. "Competition and the Core," Journal of Political Economy, University of Chicago Press, vol. 104(1), pages 85-107, February.
    6. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    7. Michael H. Rothkopf & Aleksandar Pekev{c} & Ronald M. Harstad, 1998. "Computationally Manageable Combinational Auctions," Management Science, INFORMS, vol. 44(8), pages 1131-1147, August.
    8. Roth, Ae & Verrecchia, Re, 1979. "Shapley Value As Applied To Cost Allocation - Reinterpretation," Journal of Accounting Research, Wiley Blackwell, vol. 17(1), pages 295-303.
    9. Elizabeth Baldwin & Paul Klemperer, 2019. "Understanding Preferences: “Demand Types”, and the Existence of Equilibrium With Indivisibilities," Econometrica, Econometric Society, vol. 87(3), pages 867-932, May.
    10. Karla Hoffman & Dinesh Menon, 2010. "A Practical Combinatorial Clock Exchange for Spectrum Licenses," Decision Analysis, INFORMS, vol. 7(1), pages 58-77, March.
    11. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Jacob K. Goeree & Luke Lindsay, 2012. "Designing package markets to eliminate exposure risk," ECON - Working Papers 071, Department of Economics - University of Zurich.
    13. Goeree, Jacob K. & Holt, Charles A., 2010. "Hierarchical package bidding: A paper & pencil combinatorial auction," Games and Economic Behavior, Elsevier, vol. 70(1), pages 146-169, September.
    14. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    15. M. Maschler & B. Peleg & L. S. Shapley, 1979. "Geometric Properties of the Kernel, Nucleolus, and Related Solution Concepts," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 303-338, November.
    16. Robert W. Day & Peter Cramton, 2012. "Quadratic Core-Selecting Payment Rules for Combinatorial Auctions," Operations Research, INFORMS, vol. 60(3), pages 588-603, June.
    17. Sjostrom, William, 1989. "Collusion in Ocean Shipping: A Test of Monopoly and Empty Core Model s," Journal of Political Economy, University of Chicago Press, vol. 97(5), pages 1160-1179, October.
    18. S.J. Rassenti & V.L. Smith & R.L. Bulfin, 1982. "A Combinatorial Auction Mechanism for Airport Time Slot Allocation," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 402-417, Autumn.
    19. Paul Milgrom, 2007. "Package Auctions and Exchanges," Econometrica, Econometric Society, vol. 75(4), pages 935-965, July.
    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. Van Essen, Matt & Wooders, John, 2021. "Allocating positions fairly: Auctions and Shapley value," Journal of Economic Theory, Elsevier, vol. 196(C).

    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. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press, vol. 33(4), pages 541-571.
    2. Robert W. Day & Peter Cramton, 2012. "Quadratic Core-Selecting Payment Rules for Combinatorial Auctions," Operations Research, INFORMS, vol. 60(3), pages 588-603, June.
    3. Committee, Nobel Prize, 2020. "Improvements to auction theory and inventions of new auction formats," Nobel Prize in Economics documents 2020-2, Nobel Prize Committee.
    4. Chernomaz, Kirill & Levin, Dan, 2012. "Efficiency and synergy in a multi-unit auction with and without package bidding: An experimental study," Games and Economic Behavior, Elsevier, vol. 76(2), pages 611-635.
    5. Pierre Dehez, 2017. "On Harsanyi Dividends and Asymmetric Values," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-36, September.
    6. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    7. Anthony M. Kwasnica & John O. Ledyard & Dave Porter & Christine DeMartini, 2005. "A New and Improved Design for Multiobject Iterative Auctions," Management Science, INFORMS, vol. 51(3), pages 419-434, March.
    8. Oktay Günlük & Lászlo Ladányi & Sven de Vries, 2005. "A Branch-and-Price Algorithm and New Test Problems for Spectrum Auctions," Management Science, INFORMS, vol. 51(3), pages 391-406, March.
    9. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    10. Song, Jiongjiong & Regan, A C, 2003. "Approximation Algorithms for the Bid Construction Problem in Combinatorial Auctions for the Procurement of Freight Transportation Contracts," University of California Transportation Center, Working Papers qt3j7034z2, University of California Transportation Center.
    11. Lawrence M. Ausubel & Peter Cramton & Paul Milgrom, 2012. "System and Method for a Hybrid Clock and Proxy Auction," Papers of Peter Cramton 12acmhc, University of Maryland, Department of Economics - Peter Cramton, revised 2012.
    12. Daniel Granot & Jeroen Kuipers & Sunil Chopra, 2002. "Cost Allocation for a Tree Network with Heterogeneous Customers," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 647-661, November.
    13. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "The proportional Shapley value and applications," Games and Economic Behavior, Elsevier, vol. 108(C), pages 93-112.
    14. Goeree, Jacob K. & Lien, Yuanchuan, 2014. "An equilibrium analysis of the simultaneous ascending auction," Journal of Economic Theory, Elsevier, vol. 153(C), pages 506-533.
    15. Ning Sun & Zaifu Yang, 2014. "An Efficient and Incentive Compatible Dynamic Auction for Multiple Complements," Journal of Political Economy, University of Chicago Press, vol. 122(2), pages 422-466.
    16. Peter Cramton, 2013. "Spectrum Auction Design," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 42(2), pages 161-190, March.
    17. Vohra, Rakesh V., 2015. "Combinatorial Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    18. Munro, David R. & Rassenti, Stephen J., 2019. "Combinatorial clock auctions: Price direction and performance," Games and Economic Behavior, Elsevier, vol. 117(C), pages 195-217.
    19. René Brink, 2017. "Games with a permission structure - A survey on generalizations and applications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-33, April.
    20. Kemal Guler & Martin Bichler & Ioannis Petrakis, 2016. "Ascending Combinatorial Auctions with Risk Averse Bidders," Group Decision and Negotiation, Springer, vol. 25(3), pages 609-639, May.

    More about this item

    Keywords

    Shapley value; Auctions; Exchanges; Package bidding; Balanced budget;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

    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:108:y:2018:i:c:p:170-181. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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 hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.