| L.S. Shapley. On balanced sets and cores. Naval Research Logistics Quaterly, 14:453--460. |
.... j) #(I, j) c(I) The connection between the linear programming dual and cost sharing is well known, and has been used to build core and approximate core allocations for various problems, including facility location [7, 14] and TSP games [12] In fact, the classic Bondareva Shapley theorem [6, 31] implies that for so called covering games (in which the cost c # ( is given by the minimum cost solution to a covering integer program) the core is nonempty if and only if the linear relaxation of the game defining IP has no integrality gap. Moulin and Shenker [29] show that cross monotonic ....
L.S. Shapley. On balanced sets and cores. Naval Research Logistics Quaterly, 14:453--460.
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L.S. Shapley. On balanced sets and cores. Naval Research Logistics Quaterly, 14:453--460.
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