Axiomatizing core extensions on NTU games

Abstract

We study solution concepts for NTU games, where the cooperation (or negotiation) of the players can be obtained by means of non-trivial families of coalitions (e.g. balanced families). We give an axiomatization of the aspiration core on the domain of all NTU games as the only solution that satisfies non-emptiness, individual rationality, a generalized version of consistency and independence of individual irrelevant alternatives. If we consider solutions supported by partitions, our axioms characterize the c-core [Guesnerie and Oddou in, Econ Lett 3(4):301–306, 1979; Sun et al. in, J Math Econ 44(7–8):853–860, 2008], and if we consider solutions supported only by the grand coalition, our axioms also characterize the classical core, on appropriate subdomains. The main result of this paper generalizes Peleg’s core axiomatization [J Math Econ 14(2):203–214, 1985] to non-empty solutions that are supported by non-trivial families of coalitions.