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On Proportional Excess for NTU Games

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  • Sergei Pechersky

Abstract

An axiomatic approach is developed to define the 'proportional excess' on the space of positively generated NTU games. This excess generalizes to NTU games the proportional TU excess v(S)/x(S). Five axioms are proposed, and it is shown that the proportional excess, which possess Kalai's properties except the boundary condition (it equals 1, rather than 0), is the unique excess function satisfying the axioms. The properties of proportional excess and related solutions are studied. In particular, for the proportional (pre)nucleolus a geometric characterization, which modifies the Maschler-Peleg-Shapley geometric characterization of the standard TU nucleolus, is given.

Suggested Citation

  • Sergei Pechersky, 2001. "On Proportional Excess for NTU Games," EUSP Department of Economics Working Paper Series 2001/02, European University at St. Petersburg, Department of Economics, revised 30 Oct 2001.
    • Handle: RePEc:eus:wpaper:ec2001_02
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    References listed on IDEAS

    as
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    6. 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.
    7. Lemaire, Jean, 1991. "Cooperative Game Theory and its Insurance Applications," ASTIN Bulletin, Cambridge University Press, vol. 21(1), pages 17-40, April.
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    More about this item

    Keywords

    cooperative NTU games; excess function; nucleolus; prenucleolus; (Minkowski) gauge function;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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