Geodesic
Associated consistency based on utility functions of coalitions
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 1 (2009) no. 1, pp. 87-195

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A cooperative game problem is treated as a bargaining problem with claim point. For given continuous strictly increasing utility functions of coalitions, we suppose that for every partition of the player set, the result does not change after equal sacrifice w.r.t. these functions overestimation of characteristic function values for partition members. This supposition and continuity assumption lead to a special value and give an iterative method for computation its results. In particular, for equal logarithmic utility functions of coalitions, we get proportional overestimation of characteristic functions for partition members and the value is the weighted entropy solution. The anonymity assumption and the “dummy” property give the Shapley value. The weighted entropy solution follows from the positive homogeneity assumption.
Keywords: cooperative game, weighted entropy, Shapley value. 
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     author = {Natalia Naumova},
     title = {Associated consistency based on utility functions of coalitions},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {87--195},
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     volume = {1},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2009_1_1_a4/}
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Natalia Naumova. Associated consistency based on utility functions of coalitions. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 1 (2009) no. 1, pp. 87-195. http://geodesic.mathdoc.fr/item/MGTA_2009_1_1_a4/