Consistency , anonymity , and the core on the domain of convex games ∗

Peleg (1986) and Tadenuma (1992) provide two well-known axiomatic characterizations of the core on the domain of balanced TU games. Peleg’s characterization says that the core is the only solution that satisfies non-emptiness, individual rationality, super-additivity, and a reduced game property introduced by Davis and Maschler (1965). Tadenuma’s characterization says that the core is the only solution that satisfies non-emptiness, individual rationality and a reduced game property introduced by Moulin (1985). In this note, we investigate what happens when the domain is restricted to the class of convex TU games. In particular, we show that (i) the core is not the only solution that satisfies Peleg’s four axioms and anonymity ; (ii) the core is the only solution that satisfies Peleg’s four axioms, anonymity, and additional three axioms; and (iii) the core is not the only solution that satisfies Tadenuma’s three axioms and anonymity.