论文信息 - The kernel/nucleolus of a standard tree game

The kernel/nucleolus of a standard tree game

In this paper we characterize the nucleolus (which coincides with the kernel) of a tree enterprise. We also provide a new algorithm to compute it, which sheds light on its structure. We show that in particular cases, including a chain enterprise one can compute the nucleolus in O(n) operations, wheren is the number of vertices in the tree.

[1] M. Maschler,et al. The Structure of the Kernel of a Cooperative Game , 1967 .

[2] L. Shapley. Cores of convex games , 1971 .

[3] L. Shapley,et al. The kernel and bargaining set for convex games , 1971 .

[4] S. Littlechild. A simple expression for the nucleolus in a special case , 1974 .

[5] S. C. Littlechild,et al. A further note on the nucleoous of the “airport game” , 1976 .

[6] C. G. Bird,et al. On cost allocation for a spanning tree: A game theoretic approach , 1976, Networks.

[7] S. C. Littlechild,et al. Aircraft Landing Fees: A Game Theory Approach , 1977 .

[8] Nimrod Megiddo,et al. Computational Complexity of the Game Theory Approach to Cost Allocation for a Tree , 1978, Math. Oper. Res..

[9] Daniel Granot,et al. Minimum cost spanning tree games , 1981, Math. Program..

[10] Daniel Granot,et al. On the core and nucleolus of minimum cost spanning tree games , 1984, Math. Program..

[11] B. Peleg. On the reduced game property and its converse , 1987 .

[12] M. Maschler. The bargaining set, kernel, and nucleolus , 1992 .

[13] Daniel Granot,et al. Computational Complexity of a Cost Allocation Approach to a Fixed Cost Spanning Forest Problem , 1992, Math. Oper. Res..