Credible Threats of Secession, Partnership, and Commonwealths

Abstract

We define a concept of a credible threat to secede; a group of players can credibly secede if, by secession, the group can harm a subset of the complementary coalition while maintaining its own payoff and the payoff of the remainder of the complementary coalition. The set of efficient payoffs that are immune to secession constitutes a subset of the core and may be empty even when the core is nonempty. To solve this problem and to explain the formation of not-necessarily-self-sufficient groups within larger organizations, we introduce the concept of a commonwealth — a payoff in the core and a partition of players into states so that all members of a state are mutually dependent upon each other and no state can credibly secede. We show that the commonwealth core is equivalent to the partnered core. That is, when secession is constrained to be carried out only by partnerships the two concepts coincide. As a corollary, the commonwealth core is nonempty whenever the core is nonempty.

The authors gratefully acknowledge the financial support of the Faculty of Arts and Science at the University of Pittsburgh and the Social Sciences and Humanities Research Council of Canada. We are also grateful to the University of Bonn for having us both as visitors, which lead to our collaborative research. One author is especially grateful to Reinhard Selten for many discussions of the importance of credibility of threats. Finally, we thank Howard Petith for stimulating discussions on partnership, Deidre Herrick for proposing the term “commonwealth” and Werner Girth for helpful comments on an earlier version of this paper.

This author expresses her gratitude to the Autonoma University of Barcelona and the University of Alabama for support and hospitality during the period that this paper was written.