Article1978

Computational Complexity of the Game Theory Approach to Cost Allocation for a Tree

191 citations0/0 files storedMathematics of Operations Research

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Game Theory and Voting Systems Complexity and Algorithms in Graphs Game Theory and Applications

Abstract

In the game theory approach to the problem of allocating cost, the users of a facility are viewed as players in a cooperative n-person game. It is the nature of cooperative games that the power of each one of the 2n−1 possible coalitions is taken into account. Thus, practical problems of allocating cost may be intractable in the game theory approach because of the computational complexity involved. However, it is shown that good algorithms do exist for the nucleolus and the Shapley value allocations for a tree. The nucleolus can be computed within O(n3) operations and the Shapley allocation in O(n) operations.

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References

1988A value for n -person games 1969The Nucleolus of a Characteristic Function Game 1973A Simple Expression for the Shapley Value in a Special Case 1976On cost allocation for a spanning tree: A game theoretic approach 1977Aircraft Landing Fees: A Game Theory Approach 1966A characterization, existence proof and dimension bounds for the kernel of a game

Cited by

1999Algorithmic Aspects of the Core of Combinatorial Optimization Games 1984On the core and nucleolus of minimum cost spanning tree games 2011Computational Aspects of Cooperative Game Theory 2007A fair rule in minimum cost spanning tree problems 2003Matching Games: The Least Core and the Nucleolus 2011Mechanisms for multi-level marketing 1994Chapter 34 Cost allocation 1991On the core of network synthesis games

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