Axiomatizations of the Shapley-Esl Value for Cooperative Games with Coalition Structures

Each value for TU-games satisfying efficiency, symmetric and linear is called an ESL value. We introduce a new value for TU-games with coalition structures, namely the Shapley-ESL value, which applies the Shapley value among coalitions and the ESL value within coalitions. Based on a new basis for TU-games with any given coalition structure, we propose axiomatizations of the Shapley-ESL value. The Shapley-ESL value is first axiomatized by introducing a general null player axiom (namely the β-partial null player property), together with weakened symmetries (sign coalitional symmetry, sign intracoalitional symmetry) and standard axioms of efficiency and additivity. Our another characterization is given by replacing the β-partial null player property and additivity in the first axiomatization with β-partial marginality