Axiomatizing Core Extensions

We give an axiomatization of the aspiration core on the domain of all TU-games using a relaxed feasibility condition, non-emptiness, individual rationality, and generalized versions of the reduced game property (consistency) and superadditivity. Our axioms also characterize the C-core ([Guesnerie and Oddou, 1979] and [Sun, Trockel, and Yang, 2008]) and the core on appropriate subdomains. The latter result generalizes Peleg's (1986) axiomatization to the entire family of TU-games