According to a Shapley's game-theoretical result, there exists a unique game-value of cooperative games that satisfy axioms on additivity, efficiency, null-player property and symmetry. The original setting requires the symmetry with respect to arbitrary permutations of the players. If we weaken the symmetry axiom to a symmetry with respect to a subgroup G of the permutation group S_n, the uniqueness of the game-value is satisfied if and only if the group G satisfies a special following "supertransitivity" property. Moreover, for an arbitrary hypergraph H, the Shapley's value is a unique G-symmetric quasivalue of a linear subspace. For more information see the attached PDF invitation.