On finding the nucleolus of an n-person cooperative game |
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Authors: | J. K. Sankaran |
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Affiliation: | 1. Department of Management Studies, Indian Institute of Science, 560012, Bangalore, India
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Abstract: | Kohlberg (1972) has shown how the nucleolus for ann-person game with side-payments may be found by solving a single minimization LP in case the imputation space is a polytope. However the coefficients in the LP have a very wide range even for problems with 3 or 4 players. Therefore the method is computationally viable only for small problems on machines with finite precision. Maschler et al. (1979) find the nucleolus by solving a sequence of minimization LPs with constraint coefficients of either –1, 0 or 1. However the number of LPs to be solved is o(4n). In this paper, we show how to find the nucleolus by solving a sequence of o(2n) LPs whose constraint coefficients are –1, 0 or 1. |
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