The relative interior of the base polyhedron and the core

Summary. This note provides two necessary and sufficient conditions for the relative interior of the core (and the base polyhedron) to be non-empty: (i) the second largest excess of the prenucleolus is negative; (ii) the grand coalition's payoff is greater than the minimum no-blocking payoff. Such conditions imply an intuitive method in proving core existence, they also imply results on the sensitivity of the base polyhedron and the core. Received: June 25, 1999; revised version: May 8, 2000