Compatibility in Transferable Utility Cooperative Games
17 Pages Posted: 12 Jun 2012 Last revised: 1 Nov 2012
Date Written: June 11, 2012
In this paper, we introduce the concept of the compatibility of two transferable utility cooperative games. Two games are compatible if there exists at least one allocation which belongs to the core of both games. We look at the class of nonnegative convex games where the value of the grand coalition sums to one. We conclude that for this class of games, two games are compatible if the sum of the values of the two games for all splits of the grand coalition into two is at most one. Here we use this concept of compatibility to justify why coalitions may fall apart when they are faced with two or more issues. We also do an application of this concept of compatibility to the case of EU member countries who are in ``debt crises.'' We show that the future membership of a country in the EU depends on the ``degree of importance of participation'' in a coalition. We include numerical examples as well as graphical illustrations of compatible and incompatible games.
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