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Excess Values for Cooperative Games with Transferable Utilities and Double Consistent Allocation Methods


  • Elena Yanovskaya

    () (National Research University "Higher School of Economics" St.Petersburg Branch, and St.Petersburg Institute for Economics and Mathematics, Russian Academy of Sciences, Tchaikovsky st. 1, 191187 St.Petersburg, Russia)


For cooperative games with transferable utilities (TU games) excess functions e : R2 ! R1 whose values e(x(S); v(S)); S N are relative negative utilities of coalitions S with respect to their payo s x(S) = Pi2S xi are de ned. The excess values for the class of two-person games are de ned as those giving to both players equal excess values. An extension of this de nition to the class of all TU games is given. For surplus sharing problems as a particular class of TU games, the excess values turned out to be parametric methods which are allocation-consistent. However, allocation consistency may not coincide with game theoretic consistency on the class of surplus sharing problems. Necessary and sucient conditions on the excess functions under which both de nitions of consistency { for the allocation methods and for TU game solutions { coincide on the class of surplus sharing problems are given.

Suggested Citation

  • Elena Yanovskaya, 2011. "Excess Values for Cooperative Games with Transferable Utilities and Double Consistent Allocation Methods," HSE Working papers WP BRP 10/EC/2011, National Research University Higher School of Economics.
  • Handle: RePEc:hig:wpaper:10/ec/2011

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    References listed on IDEAS

    1. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, vol. 36(1), pages 120-148, June.
    2. Theo Driessen & Elena Yanovskaya, 2002. "Note On linear consistency of anonymous values for TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 601-609.
    3. Morton Davis & Michael Maschler, 1965. "The kernel of a cooperative game," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 12(3), pages 223-259, September.
    4. Elena Yanovskaya, 2002. "Consistency For Proportional Solutions," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 343-356.
    5. Ruiz, Luis M. & Valenciano, Federico & Zarzuelo, Jose M., 1998. "The Family of Least Square Values for Transferable Utility Games," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 109-130, July.
    6. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
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    More about this item


    Allocation problem; Allocation method; Surplus sharing problem; TU game solution; Excess function; Excess value; Consistency;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement


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