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Shapley value based pricing for auctions and exchanges

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  • 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
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    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, President and Fellows of Harvard College, 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. Lester G. Telser, 1994. "The Usefulness of Core Theory in Economics," Journal of Economic Perspectives, American Economic Association, vol. 8(2), pages 151-164, Spring.
    10. 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.
    11. Karla Hoffman & Dinesh Menon, 2010. "A Practical Combinatorial Clock Exchange for Spectrum Licenses," Decision Analysis, INFORMS, vol. 7(1), pages 58-77, March.
    12. 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).
    13. Jacob K. Goeree & Luke Lindsay, 2012. "Designing package markets to eliminate exposure risk," ECON - Working Papers 071, Department of Economics - University of Zurich.
    14. 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.
    15. 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.
    16. 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.
    17. Robert W. Day & Peter Cramton, 2012. "Quadratic Core-Selecting Payment Rules for Combinatorial Auctions," Operations Research, INFORMS, vol. 60(3), pages 588-603, June.
    18. 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.
    19. 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.
    20. Paul Milgrom, 2007. "Package Auctions and Exchanges," Econometrica, Econometric Society, vol. 75(4), pages 935-965, July.
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    Cited by:

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    2. Van Essen, Matt & Wooders, John, 2021. "Allocating positions fairly: Auctions and Shapley value," Journal of Economic Theory, Elsevier, vol. 196(C).

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    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

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