Introduction to algorithms
Mathematics of Operations Research
An algorithm for finding the nucleolus of assignment games
International Journal of Game Theory
The reactive bargaining set of some flow games and of superadditive simple games
International Journal of Game Theory
On the complexity of testing membership in the core of min-cost spanning tree games
International Journal of Game Theory
The nucleon of cooperative games and an algorithm for matching games
Mathematical Programming: Series A and B
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Matching games: the least core and the nucleolus
Mathematics of Operations Research
Finding nucleolus of flow game
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Algorithms for core stability, core largeness, exactness, and extendability of flow games
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Hi-index | 0.00 |
Using the ellipsoid method, both Deng et al. [Deng, X., Q. Fang, X. Sun. 2006. Finding nucleolus of flow game. Proc. 17th ACM-SIAM Sympos. Discrete Algorithms. ACM Press, New York, 124--131] and Potters et al. [Potters, J., H. Reijnierse, A. Biswas. 2006. The nucleolus of balanced simple flow networks. Games Econom. Behav.54 205--225] show that the nucleolus of simple flow games (where all edge capacities are equal to one) can be computed in polynomial time. Our main result is a combinatorial method based on eliminating redundant s--t path constraints such that only a polynomial number of constraints remains. This leads to efficient algorithms for computing the core, nucleolus, and nucleon of simple flow games. Deng et al. also prove that computing the nucleolus for (general) flow games is NP-hard. We generalize this by proving that computing the f-nucleolus of flow games is NP-hard for all priority functions f that satisfy f(A) 0 for all coalitions A with worth v(A) 0 (so, including the priority functions corresponding to the nucleolus, nucleon, and per-capita nucleolus).