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THE EGALITARIAN NON-k-AVERAGED CONTRIBUTION(ENkAC-)VALUE FOR TU-GAMES

Author

Listed:
  • TSUNEYUKI NAMEKATA

    (Department of Information and Management Science, Otaru University of Commerce, 3-5-21 Midori, Otaru, Hokkaido 047-8501, Japan)

  • THEO S. H. DRIESSEN

    (Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands)

Abstract

This paper deals in a unified way with the solution concepts for transferable utility games known as the Centre of the Imputation Set value (CIS-value), the Egalitarian Non-Pairwise-Averaged Contribution value (ENPAC-value) and the Egalitarian Non-Separable Contribution value (ENSC-value). These solutions are regarded as the egalitarian division of the surplus of the overall profits after each participant is conceded to get his individual contribution specified in a respective manner. We offer two interesting individual contributions (lower- and upper-k-averaged contribution) based on coalitions of sizek(k ∈ {1,…,n-1})and introduce a new solution concept called the Egalitarian Non-k-Averaged Contribution value (ENkAC-value). CIS-, ENPAC- and ENSC-value are the same asEN1AC-,ENn-2AC-andENn-1AC-value respectively. It turns out that the lower- and the upper-k-averaged contribution form a lower- and an upper-bound of the Core respectively. The Shapley value is the centre of gravity ofn-1points;EN1AC-,…,ENn-1AC-value.ENkAC-value of the dual game is equal toENn-kAC-value of the original game. We provide a sufficient condition on the transferable utility game to guarantee that theENkAC-value coincides with the well-known solution called prenucleolus. The condition requires that the largest excesses at theENkAC-value are attained at thek-person coalitions, whereas the excesses ofk-person coalitions at theENkAC-value do not differ.

Suggested Citation

  • Tsuneyuki Namekata & Theo S. H. Driessen, 1999. "THE EGALITARIAN NON-k-AVERAGED CONTRIBUTION(ENkAC-)VALUE FOR TU-GAMES," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 45-61.
    • Handle: RePEc:wsi:igtrxx:v:01:y:1999:i:01:n:s0219198999000050
    DOI: 10.1142/S0219198999000050
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    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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