Advertisement

Reduced Game Property of Linear Values with Equal Treatment Property

  • Tsuneyuki Namekata
  • Theo S.H. Driessen
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 43)

Abstract

A transferable utility game deals with problems of how to allocate the total benefit among players by considering contributions of various coalitions of players to the total benefit. A value for games is an allocation of the total benefit among them. Many values such as the Shapley value and the prenucleolus are introduced by their own equity consideration. Thus a consistency in terms of a reduced game is a useful tool to compare various solutions in a unified way, because it expresses the differences in solutions as those in associated reduced games. This paper axiomatizes linear values with Equal Treatment Property by the consistency in terms of a reduced game.

Keywords

TU-game consistency reduced game Shapley value Solidarity value. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Driessen, T. S. H. and Funaki, Y. “Reduced Game Properties of Egalitarian Division Rules for TU-games.” In eds T. Parthasarathy, B. Dutta, J. A. M. Potters, T. E. S. Raghavan, D. Ray and A. Sen. Game Theoretical Applications to Economics and Operations Research, Dordrecht: Kluwer Academic Publisher, 1997Google Scholar
  2. Driessen, T. S. H. A Survey of Consistency Properties in Cooperative Game Theory. SIAM Review 1991; 33: 43–59CrossRefGoogle Scholar
  3. Namekata, T. and Driessen, T. S. H. The Egalitarian Non-k-Averaged Contribution (EnkAC-) value for TU-Games. International Game Theory Review 1999; 1: 45–61CrossRefGoogle Scholar
  4. Namekata, T. and Driessen, T. S. H. Reduced Game Property of the Egalitarian Non-k-Averaged Contribution (ENkAC-) Value and the Shapley Value. International Transactions in Operational Research 2000; 7: 365–382Google Scholar
  5. Nowak, A. S. and Radzik, T. A Solidarity Value for n-Person Transferable Utility Games. International Journal of Game Theory 1994; 23: 43–48CrossRefGoogle Scholar
  6. Ruiz, L. M., Valenciano, F. and Zarzuelo, J. M. The Least Square Prenucleolus and the Least Square Nucleolus. Two Values for TU Games Based on the Excess Vector. International Journal of Game Theory 1996; 25: 113–134CrossRefGoogle Scholar
  7. Ruiz, L. M., Valenciano, F. and Zarzuelo, J. M. The Family of Least Square Values for Transferable Utility Games. Games and Economic Behavior 1998; 24: 109–130CrossRefGoogle Scholar
  8. Thomson, W. Consistent Allocation Rules. Rochester Center for Economics Research Working Paper No. 418 1996Google Scholar
  9. Young, H. P. On dividing an amount according to individual claims or liabilities. Mathematics of Operations Research 1987; 12: 398–414CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Tsuneyuki Namekata
    • 1
  • Theo S.H. Driessen
    • 2
  1. 1.Department of Information and Management ScienceOtaru University of CommerceOtaru HokkaidoJapan
  2. 2.Faculty of Mathematical SciencesUniversity of TwenteEnschedeThe Netherlands

Personalised recommendations