Justin Toth (University of Waterloo): A General Framework For Computing the Nucleolus Via Dynamic Programming

In a cooperative game when the problem of computing the minimum excess coalition for a given allocation can be formulated as a dynamic program we show that the nucleolus can be computed in time polynomial in the size of the dynamic program. This gives a general technique for designing efficient algorithms for computing the nucleolus of a cooperative game. This technique is inspired by a recent result of Pashkovich on weighted voting games. However, our technique significantly extends beyond the capabilities of previous work. We demonstrate this by applying it to give an algorithm for computing the nucleolus of b-matching games in polynomial time on graphs of bounded treewidth.

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