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Minimum Cost Spanning Tree Games
, 2001
"... most grateful to two anonymous referees and an Associate Editor for remarkably detailed comments on an earlier version of the paper. We also acknowledge helpful suggestions from A.van den Nouweland and H. Moulin. We propose a new cost allocation rule for minimum cost spanning tree games. The new rul ..."
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most grateful to two anonymous referees and an Associate Editor for remarkably detailed comments on an earlier version of the paper. We also acknowledge helpful suggestions from A.van den Nouweland and H. Moulin. We propose a new cost allocation rule for minimum cost spanning tree games. The new
The Stackelberg Minimum Spanning Tree Game
 In Proc. of 10th WADS
, 2007
"... Abstract. We consider a oneround twoplayer network pricing game, the Stackelberg Minimum Spanning Tree game or StackMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed cost (representing the competitor’ ..."
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Cited by 13 (1 self)
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Abstract. We consider a oneround twoplayer network pricing game, the Stackelberg Minimum Spanning Tree game or StackMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed cost (representing the competitor
Cost Monotonicity, Consistency And Minimum Cost Spanning Tree Games
 GAMES AND ECONOMIC BEHAVIOR
, 2002
"... We propose a new cost allocation rule for minimum cost spanning tree games. The new rule is a core selection and also satisfies cost monotonicity. We also give characterization theorems for the new rule as well as the muchstudied Bird allocation. We show that the principal difference between these ..."
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Cited by 19 (0 self)
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We propose a new cost allocation rule for minimum cost spanning tree games. The new rule is a core selection and also satisfies cost monotonicity. We also give characterization theorems for the new rule as well as the muchstudied Bird allocation. We show that the principal difference between
Reduction of ultrametric minimum cost spanning tree games to cost allocation games on rooted trees
 Research Institute for Mathematical Sciences, Kyoto University
, 2009
"... Abstract A minimum cost spanning tree game is called ultrametric if the cost function on the edges of the underlying network is an ultrametric. We show that every ultrametric minimum cost spanning tree game is reduced to a cost allocation game on a rooted tree. It follows that there exist O(n2) time ..."
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Cited by 1 (1 self)
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Abstract A minimum cost spanning tree game is called ultrametric if the cost function on the edges of the underlying network is an ultrametric. We show that every ultrametric minimum cost spanning tree game is reduced to a cost allocation game on a rooted tree. It follows that there exist O(n2
Representation of Ultrametric Minimum Cost Spanning Tree Games as Cost Allocation Games on Rooted Trees
"... A minimum cost spanning tree game is called ultrametric if the cost function on the edges of the underlying network is an ultrametric. We show that every ultrametric minimum cost spanning tree game is represented as a (ost allocation game on a rooted tree and give an $O(??^{2}) $ time algorithm to ..."
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A minimum cost spanning tree game is called ultrametric if the cost function on the edges of the underlying network is an ultrametric. We show that every ultrametric minimum cost spanning tree game is represented as a (ost allocation game on a rooted tree and give an $O(??^{2}) $ time algorithm
Computation of the Shapley Value of Minimum Cost Spanning Tree Games: #PHardness and Polynomial Cases
, 2010
"... We show that computing the Shapley value of minimum cost spanning tree games is #Phard even if the cost functions are restricted to be {0, 1}valued. The proof is by a reduction from counting the number of minimum 2terminal vertex cuts of an undirected graph, which is #Pcomplete. We also investig ..."
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Cited by 2 (0 self)
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We show that computing the Shapley value of minimum cost spanning tree games is #Phard even if the cost functions are restricted to be {0, 1}valued. The proof is by a reduction from counting the number of minimum 2terminal vertex cuts of an undirected graph, which is #Pcomplete. We also
On The Complexity Of Testing Membership In The Core Of MinCost Spanning Tree Games
 INTERNATIONAL JOURNAL OF GAME THEORY
, 1994
"... Let N = f1, ..., ng be a finite set of players and KN the complete graph on the node set N [ f0g. Assume that the edges of KN have nonnegative weights and associate with each coalition S ` N of players as cost c(S) the weight of a minimal spanning tree on the node set S [ f0g. Using reduction to EXA ..."
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Cited by 36 (8 self)
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Let N = f1, ..., ng be a finite set of players and KN the complete graph on the node set N [ f0g. Assume that the edges of KN have nonnegative weights and associate with each coalition S ` N of players as cost c(S) the weight of a minimal spanning tree on the node set S [ f0g. Using reduction
Note on the Computational Complexity of Least Core Concepts for MinCost Spanning Tree Games
 UNIVERSITY OF TWENTE
, 1999
"... 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 NPhard for minimum cost spannning tree games. As a consequence, computing the nucleolu ..."
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Cited by 7 (1 self)
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the nucleolus, the nucleon and the percapita nucleolus of minimum cost spanning tree games is also NPhard.
Submodularity of MinimumCost Spanning Tree
"... We give a necessary condition and a sufficient condition for a minimumcost spanning tree game introduced by Bird to be submodular (or convex). When the cost is restricted to two values, we give a characterization of submodular minimumcost spanning tree games. We also discuss algorithmic issues. ..."
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We give a necessary condition and a sufficient condition for a minimumcost spanning tree game introduced by Bird to be submodular (or convex). When the cost is restricted to two values, we give a characterization of submodular minimumcost spanning tree games. We also discuss algorithmic issues.
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