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

Author

Listed:
  • 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)

Abstract

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
    as

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    File URL: http://www.hse.ru/data/2012/01/17/1260439375/Elena%20Yanovskaya_Excess%20values%20for%20cooperative%20games%20with.pdf
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    References listed on IDEAS

    as
    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. repec:wsi:igtrxx:v:04:y:2002:i:03:n:s0219198902000744 is not listed on IDEAS
    4. 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.
    5. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    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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