An axiomatization of the core of cooperative games without side payments (Q1068733)

Let \(M\) be a set of \(m\) players, \(m\geq 3\), and let \(\Gamma\) be the set of all (finite) games (without side payments) that have a non-empty core. When \(M\) is finite, the following four (independent) axioms fully characterize the core on \(\Gamma\) : (i) non-emptiness, (ii) individual rationality, (iii) the reduced game property, and (iv) the converse reduced game property. If \(M\) is infinite, then the converse reduced game property is redundant.