Potentializability and consistency for multi-choice solutions

The paper introduces and discusses several characterizations of the multi-choice Shapley value (introduced by Nouweland et al. in ZOR-Math Methods Oper Res 41:289–311, 1995), on the domain of multi-choice games. These characterizations generalize the potential approach and results of Calvo and Santos (Math Soc Sci 34:175–190, 1997) into this domain, and the relations are treated with the axiomatic approach in Calvo and Santos (Math Soc Sci 40:341–354, 2000). Also, based on the axioms of two-person standardness and consistency, we offer an axiomatization of the multi-choice Shapley value. The authors are grateful to Professor Sjaak Hurkens and the anonymous referees for very helpful suggestions and comments.