, Volume 18, Issue 3, pp 635-648

The relative interior of the base polyhedron and the core

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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