Abstract
We develop two efficient procedures for generating cost allocation vectors in the core of a minimum cost spanning tree (m.c.s.t.) game. The first procedure requires O(n 2) elementary operations to obtain each additional point in the core, wheren is the number of users. The efficiency of the second procedure, which is a natural strengthening of the first procedure, stems from the special structure of minimum excess coalitions in the core of an m.c.s.t. game. This special structure is later used (i) to ease the computational difficulty in computing the nucleolus of an m.c.s.t. game, and (ii) to provide a geometric characterization for the nucleolus of an m.c.s.t. game. This geometric characterization implies that in an m.c.s.t. game the nucleolus is the unique point in the intersection of the core and the kernel. We further develop an efficient procedure for generating fair cost allocations which, in some instances, coincide with the nucleolus. Finally, we show that by employing Sterns' transfer scheme we can generate a sequence of cost vectors which converges to the nucleolus.
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Part of this research was done while the author was visiting the Department of Operations Research at Stanford University. This research was partially supported by Natural Sciences and Engineering Research Council Canada Grant A-4181.
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Granot, D., Huberman, G. On the core and nucleolus of minimum cost spanning tree games. Mathematical Programming 29, 323–347 (1984). https://doi.org/10.1007/BF02592000
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DOI: https://doi.org/10.1007/BF02592000