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 quasi-values 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.