A note on an axiomatization of the core of market games

As shown by Peleg, the core of market games is characterized by nonemptiness, individual rationality, superadditivity, the weak reduced game property, the converse reduced game property, and weak symmetry. It was not known whether weak symmetry was logically independent. With the help of a certain transitive 4-person transitive utility game, it is shown that weak symmetry is redundant in this result. Hence, the core on market games is axiomatized by the remaining five properties, if the universe of players contains at least four members.