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Games With Identical Shapley Values

Author

Listed:
  • Sylvain Béal

    (Université de Bourgogne Franche-Comté, CRESE)

  • Mihai Manea

    (State University of New York at Stony Brook)

  • Eric Rémila

    (Université de Saint-Etienne, Gate)

  • Phillippe Solal

    (Université de Saint-Etienne, Gate)

Abstract

We discuss several sets of cooperative games in which the Shapley value assigns zero payo s to all players. Each set spans the kernel of the Shapley value and leads to a different characterization of games with identical Shapley values. The special games we identify deliver intuitive axiomatizations of the Shapley value. We explain how each basis of the kernel of the Shapley value can be augmented to construct a basis of the space of all games.

Suggested Citation

  • Sylvain Béal & Mihai Manea & Eric Rémila & Phillippe Solal, 2018. "Games With Identical Shapley Values," Working Papers 2018-03, CRESE.
    • Handle: RePEc:crb:wpaper:2018-03
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    References listed on IDEAS

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    1. Dragan, I. & Potters, J.A.M. & Tijs, S.H., 1989. "Superadditivity for solutions of coalitional games," Other publications TiSEM 283e2594-e3a0-418d-ae5e-2, Tilburg University, School of Economics and Management.
    2. Ulrich Faigle & Michel Grabisch, 2016. "Bases and linear transforms of TU-games and cooperation systems," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 875-892, November.
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    5. Yokote, Koji & Funaki, Yukihiko & Kamijo, Yoshio, 2016. "A new basis and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 21-24.
    6. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    7. Sylvain Béal & Eric Rémila & Philippe Solal, 2016. "Characterizations of Three Linear Values for TU Games by Associated Consistency: Simple Proofs Using the Jordan Normal Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-21, March.
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    More about this item

    Keywords

    Shapley value; kernel; axiomatization; factious oligarchies; paper tigers;
    All these keywords.

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