O.N. Bondareva. Some applications of linear programming to cooperative games. Problemy Kibernetiki, 10:119--139, 1963 Home/Search Document Not in Database Summary Related Articles Check |
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Group Strategyproof Mechanisms via Primal-Dual Algorithms - Pal, Tardos (2003) (8 citations) (Correct)
.... 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 ....
O. N. Bondareva. Some applications of linear programming to cooperative games. Problemy Kibernetiki, 10:119--139, 1963
Applications of Approximation Algorithms to Cooperative Games - Jain, Vazirani (2001) (30 citations) (Correct)
....of all users and C : 2 U R is a cost function. C is said to exhibit the covering property if for any set S of users and any covering of S of the form S = S j f j Delta S j , we have C(S) P j f j Delta C(S j ) where each S j is a set of users. The classic Bondareva Shapley Theorem [3, 30] shows that a necessary and sufficient condition for the existence of a weakly cross monotonic cost sharing method is that the underlying cost function exhibit the covering property. Does a cost function satisfying the covering property always admit a cross monotonic cost sharing method A ....
....cone is required. If our open problem resolves positively, the optimal cost function for LP P admits a cross monotonic cost sharing method. Multiplying by ff gives us an ff approximate budget balanced group strategyproof cost sharing mechanism. Using Lemma 7 and the Bondareva Shapley Theorem [3, 30] one can show that there exists an ff approximate weakly cross monotonic cost sharing method for Pi. However, their theorem uses an exponential sized LP which may be solvable in polynomial time in particular cases, though not in general. The following theorem gives a way of finding one such ....
O. N. Bondareva. Some applications of linear programming to cooperative games. Problemy Kibernetiki, 10:119--139, 1963.
Group Strategyproof Mechanisms via Primal-Dual Algorithms - Pal, Tardos (2003) (8 citations) (Correct)
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O.N. Bondareva. Some applications of linear programming to cooperative games. Problemy Kibernetiki, 10:119--139, 1963
Lower Bounds for Cost Sharing and Group-Strategyproof.. - Immorlica, Mahdian.. (1 citation) (Correct)
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O.N. Bondareva. Some applications of linear programming to cooperative games. Problemy Kibernetiki, 1963.
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