On the Axioms for a Cooperative Game without Side Payments

Introduction. In 1960 a set of axioms for cooperative games without side payments was suggested by Aumann and Peleg [l] which provides a neat generalization of the classical von Neumann-Morgenstern «-person theory [S]. In subsequent papers [2], [3], and [4], many results parallel to the classical theory have been proven in this new framework. The purpose of this note is to re-examine the axioms in light of a specific six-person game and to suggest a small and reasonable change in these axioms that will make the theory even more satisfying. In particular, it will be shown that this game has no von Neumann-Morgenstern solution so if there is to be any hope of a general existence theorem for solutions, the axioms need to be strengthened to exclude this example.