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Francesc Llerena and Marina Nunez
''A geometric characterization of the nucleolus of the assignment game''
( 2011, Vol. 31 No.4 )
Maschler et al. (1979) provide a geometrical characterization for the intersection of the kernel and the core of a coalitional game, showing that those allocations that lie in both sets are always the midpoint of certain bargaining range between each pair of players. In the case of the assignment game, this means that the kernel can be determined as those core allocations where the maximum amount, that can be transferred without getting outside the core, from one agent to his/her optimally matched partner equals the maximum amount that he/she can receive from this partner, also remaining inside the core (Rochford, 1984). We now prove that the nucleolus of the assignment game can be characterized by requiring this bisection property be satisfied not only for optimally matched pairs but also for optimally matched coalitions.
Keywords: assignment game, core, kernel, nucleolus
Manuscript Received : Sep 20 2011 Manuscript Accepted : Dec 05 2011

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