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Computing the NTU-Shapley value of NTU-games defined by multiple objective linear programs

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Abstract.

In this paper we study a class of cooperative games with non-transferable utility (NTU) derived from multiple objective linear programs (MOLP's). This is done in order to introduce the NTU-Shapley value as a solution to multiple objective linear programming.  We present an algorithm for the computation of the set of all NTU-Shapley values for the bicriterion cases, which is based on the simplex algorithm. Furthermore, we give a new optimal recursive procedure for the computation of the Shapley value of TU-games.

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Authors and Affiliations

  1. Department of Operations Research, University of Aarhus, building 530, Ny Munkegade, DK-8000 Århus C, Denmark (e-mail: kima@imf.au.dk), , , , , , DK

    Kim Allan Andersen & Mikael Lind

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  1. Kim Allan Andersen
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  2. Mikael Lind
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Received: September 1997/Final version: May 1999

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Andersen, K., Lind, M. Computing the NTU-Shapley value of NTU-games defined by multiple objective linear programs. Game Theory 28, 585–597 (1999). https://doi.org/10.1007/s001820050127

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  • DOI: https://doi.org/10.1007/s001820050127

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