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Persistent link: https://www.econbiz.de/10010993383
A matching game is a cooperative game (N; v) defined on a graph G = (N;E) with an edge weighting w : E ! R+. The player set is N and the value of a coalition S N is dened as the maximum weight of a matching in the subgraph induced by S. First we present an O(nm+n2 log n) algorithm that tests if...
Persistent link: https://www.econbiz.de/10010551502
The stable roommates problem with payments has as input a graph G(E,V) with an edge weighting w:E_ùR+ and the problem is to find a stable solution. A solution is a matching M with a vector p.RV that satisfies pu+pv=w(uv) for all uv.M and pu=0 for all u unmatched in M. A solution is stable if it...
Persistent link: https://www.econbiz.de/10011070719
Various least core concepts including the classical least core of cooperative games are discussed. By a reduction from minimum cover problems, we prove that computing an element in these least cores is in general NP-hard for minimum cost spanning tree games. As a consequence, computing the...
Persistent link: https://www.econbiz.de/10010847966
Various least core concepts including the classical least core of cooperative games are discussed. By a reduction from minimum cover problems, we prove that computing an element in these least cores is in general NP-hard for minimum cost spanning tree games. As a consequence, computing the...
Persistent link: https://www.econbiz.de/10010999970
Two extensions of the Shapley value are given. First we consider a probabilistic framework in which certain consistent allocation rules such as the Shapley value are characterized. The second generalization of the Shapley value is an extension to the structure of posets by means of a recursive...
Persistent link: https://www.econbiz.de/10010847824
Two extensions of the Shapley value are given. First we consider a probabilistic framework in which certain consistent allocation rules such as the Shapley value are characterized. The second generalization of the Shapley value is an extension to the structure of posets by means of a recursive...
Persistent link: https://www.econbiz.de/10010950222
The lexicographic kernel of a game lexicographically maximizes the surplusses s ij (rather than the excesses as would the nucleolus) and is contained in both the least core and the kernel. We show that an element in the lexicographic kernel can be computed efficiently, provided we can...
Persistent link: https://www.econbiz.de/10010847867
The Dreyfus–Wagner algorithm is a well-known dynamic programming method for computing minimum Steiner trees in general weighted graphs in time O * (3 k ), where k is the number of terminal nodes to be connected. We improve its running time to O * (2.684 k ) by showing that the optimum Steiner...
Persistent link: https://www.econbiz.de/10010847995
The lexicographic kernel of a game lexicographically maximizes the surplusses s <Subscript> ij </Subscript> (rather than the excesses as would the nucleolus) and is contained in both the least core and the kernel. We show that an element in the lexicographic kernel can be computed efficiently, provided we can...</subscript>
Persistent link: https://www.econbiz.de/10010999872