Communications to the Editor—A Counterexample in Game Theory

This note describes a 5-person von Neumann-Morgenstern game which has a unique solution that is strictly larger than its core. This game provides a counterexample for the following two conjectures stated by L. S. Shapley in [Kuhn, H. W., ed. Report of an Informal Conference on the Theory of n-Person Games, held at Princeton University, March 20–21, 1953 (dittoed).].