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The Shapley value in the Knaster gain game

Author

Listed:
  • Federica Briata

    (University of Genova)

  • Andrea Dall’Aglio

    (Sapienza University of Rome)

  • Marco Dall’Aglio

    (LUISS University)

  • Vito Fragnelli

    (University of Eastern Piedmont)

Abstract

In Briata et al. (AUCO Czech Econ Rev 6:199–208, 2012), the authors introduce a cooperative game with transferable utility for allocating the gain of a collusion among completely risk-averse agents involved in the fair division procedure introduced by Knaster (Ann Soc Pol Math 19:228–230, 1946). In this paper we analyze the Shapley value (Shapley, in: Kuhn, Tucker (eds) Contributions to the theory of games II (Annals of Mathematics Studies 28), Princeton University Press, Princeton, 1953) of the game and propose its use as a measure of the players’ attitude towards collusion. Furthermore, we relate the sign of the Shapley value with the ranking order of the players’ evaluation, and show that some players in a given ranking will always deter collusion. Finally, we characterize the coalitions that maximize the gain from collusion, and suggest an ad-hoc coalition formation mechanism.

Suggested Citation

  • Federica Briata & Andrea Dall’Aglio & Marco Dall’Aglio & Vito Fragnelli, 2017. "The Shapley value in the Knaster gain game," Annals of Operations Research, Springer, vol. 259(1), pages 1-19, December.
    • Handle: RePEc:spr:annopr:v:259:y:2017:i:1:d:10.1007_s10479-017-2651-8
    DOI: 10.1007/s10479-017-2651-8
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    References listed on IDEAS

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    1. Sergiu Hart, 2006. "Shapley Value," Discussion Paper Series dp421, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Federica Briata & Marco Dall’Aglio & Vito Fragnelli, 2012. "Dynamic Collusion and Collusion Games in Knaster’s Procedure," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 6(3), pages 199-208, October.
    3. Rodica Branzei & Vito Fragnelli & Ana Meca & Stef Tijs, 2009. "On Cooperative Games Related To Market Situations And Auctions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(04), pages 459-470.
    4. Graham, Daniel A & Marshall, Robert C, 1987. "Collusive Bidder Behavior at Single-Object Second-Price and English Auctions," Journal of Political Economy, University of Chicago Press, vol. 95(6), pages 1217-1239, December.
    5. Vito Fragnelli & Ana Meca, 2010. "A Note On The Computation Of The Shapley Value For Von Neumann–Morgenstern Market Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 287-291.
    6. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446, October.
    7. Vito Fragnelli & Maria Erminia Marina, 2009. "Strategic Manipulations and Collusions in Knaster Procedure," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 3(2), pages 143-153, July.
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    Cited by:

    1. Dan C. Popescu & Philip Kilby, 2020. "Approximation of the Shapley value for the Euclidean travelling salesman game," Annals of Operations Research, Springer, vol. 289(2), pages 341-362, June.

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