Complexity in cooperative game theory

We introduce cooperative games (N; v) with a description polynomial in n; where n is the number of players. In order to study the complexity of cooperative game problems, we assume that a cooperative game v : 2N ! Q is given by an oracle returning v (S) for each query S μ N: Finally, we consider several cooperative game problems and we give a list of complexity results.

[1]  Jeroen Kuipers,et al.  Computing the nucleolus of some combinatorially-structured games , 2000, Math. Program..

[2]  Sándor P. Fekete,et al.  On the complexity of testing membership in the core of min-cost spanning tree games , 1997, Int. J. Game Theory.

[3]  U. Faigle,et al.  On the complexity of testing membership in the core of min-cost spanning tree games , 1997 .

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

[5]  R. Graham,et al.  Handbook of Combinatorics , 1995 .

[6]  Jeroen Kuipers,et al.  Note Computing the nucleolus of min-cost spanning tree games is NP-hard , 1998, Int. J. Game Theory.

[7]  Robert E. Tarjan,et al.  Fibonacci heaps and their uses in improved network optimization algorithms , 1984, JACM.

[8]  T. Raghavan,et al.  An algorithm for finding the nucleolus of assignment games , 1994 .

[9]  Leslie G. Valiant,et al.  The Complexity of Enumeration and Reliability Problems , 1979, SIAM J. Comput..

[10]  Daniel Granot,et al.  Characterization sets for the nucleolus , 1998, Int. J. Game Theory.

[11]  G. Owen,et al.  The kernel/nucleolus of a standard tree game , 1996 .

[12]  Theo S. H. Driessen,et al.  On Computing the Nucleolus of a Balanced Connected Game , 1998, Math. Oper. Res..

[13]  Toshihide Ibaraki,et al.  Complexity of the Minimum Base Game on Matroids , 1997, Math. Oper. Res..

[14]  Xiaotie Deng,et al.  On the Complexity of Cooperative Solution Concepts , 1994, Math. Oper. Res..

[15]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1981 .

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

[17]  Éva Tardos,et al.  Combinatorics in computer science , 1996 .

[18]  U. Faigle,et al.  An efficient algorithm for nucleolus and prekernel computation in some classes of TU-games , 1998 .