The Shapley value: a summary of results Collected by Michel GRABISCH

Nota: this compilation of various results has been intended primarily for my personal use, hence its very rough form. It is just a quick reference compilation of results. It is far to be complete, and does not intend to be so especially for references, and I update it from time to time. All comments, discovered mistakes, etc. are welcome. Please be kind enough to cite it in references if you use it. 1 Classical coalitional games 1.1 The classical Shapley value N: = [n] set of players, v a game on 2N. The Shapley value is defined as φi(v):= S⊆N\i s!(n − s − 1)! n! [v(S ∪ i) − v(S)]. (1) Other expressions: φi(v)