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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
    1. Pechersky, Sergei & Sobolev, Arkady, 1995. "Set-Valued Nonlinear Analogues of the Shapley Value," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(1), pages 57-78.
    2. Pechersky, Sergei & Rubinov, Alexander, 1993. "Solution concept for generalized multi- stage games without side payments," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 403-420.
    3. K. Michael Ortmann, 2000. "The proportional value for positive cooperative games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 235-248, April.
    4. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, vol. 53(3), pages 599-612, May.
    5. Fisher,Franklin M. & Shell,Karl, 1998. "Economic Analysis of Production Price Indexes," Cambridge Books, Cambridge University Press, number 9780521556231, October.
    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.
    8. Maschler, Michael, 1992. "The bargaining set, kernel, and nucleolus," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 18, pages 591-667, Elsevier.
    9. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
    10. Barry Feldman, 2000. "The Proportional Value of a Cooperative Game," Econometric Society World Congress 2000 Contributed Papers 1140, Econometric Society.
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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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