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On the nucleolus of NTU-games defined by multiple objective linear programs

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Abstract

In this article we derive a class of cooperative games with non-transferable utility from multiple objective linear programs. This is done in order to introduce the nucleolus, a solution concept from cooperative game theory, as a solution to multiple objective linear problems.

We show that the nucleolus of such a game is a singleton, which is characterized by inclusion in the least core and the reduced game property. Furthermore the nucleolus satisfies efficiency, anonymity and strategic equivalence.

We also present a polynomially bounded algorithm for computation of the nucleolus. Letn be the number of objective functions. The nucleolus is obtained by solving at most2n linear programs. Initially the ideal point is computed by solvingn linear programs. Then a sequence of at mostn linear programs is solved, and the nucleolus is obtained as the unique solution of the last program.

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Authors and Affiliations

  1. Department of Operations Research, Institute of Mathematics, University of Aarhus, Building 530, Ny Munkegade, 8000, Aarhus C, Denmark

    Flemming Christensen & Mikael Lind

  2. Institute of Mathematics, University of Copenhagen, H.C. Orsted Institute, Universitetsparken 5, 2100, Copenhagen 0, Denmark

    Jørgen Tind

Authors
  1. Flemming Christensen
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  2. Mikael Lind
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  3. Jørgen Tind
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Additional information

Financial support from Nordic Academy for Advanced Study (NorFA) is gratefully acknowledged. Part of this work was done during autumn 1993 at Institute of Finance and Management Science, Norwegian School of Economics and Business Administration.

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Christensen, F., Lind, M. & Tind, J. On the nucleolus of NTU-games defined by multiple objective linear programs. Mathematical Methods of Operations Research 43, 337–352 (1996). https://doi.org/10.1007/BF01194552

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  • DOI: https://doi.org/10.1007/BF01194552

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