Dissection of solutions in cooperative game theory using representation techniques

We compute a decomposition for the space of cooperative TU-games under the action of the symmetric group S-n. In particular we identify all irreducible subspaces that are relevant to the study of symmetric linear solutions namely those that are isomorphic to the irreducible summands of R-n. We then use such decomposition to derive, in a very economical way, some old and some new results for linear symmetric solutions.