Quasi-Values on Subspaces

Quasi-values are operators satisfying all axioms of the Shapley value with the possible exception of symmetry. We introduce the characterization and extendability problems for quasivalues on linear subspaces of games, provide equivalence theorems for these problems, and show that a quasi-value on a subspace Q is extendable to the space of all games iff it is extendable to Q+Sp{u} for every game u. Finally, we characterize restrictable subspaces and solve the characterization problem for those which are also monotone.