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This material has been published in Understanding Strategic Interaction: Essays in Honor of Reinhard Selten eds. W. Guth, P. Hammerstein, B. Moldovanu, E. Van Damme, Springer -Verlag Berlin/Heidelberg/New York/Tokyo (1996) 305-312, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Springer-Verlag. Copyright (C) 1996 by Springer-Verlag, Inc.).

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Credible Threats of Secession, Partnership, and Commonwealths Philip J. Reny
Department of Economics
University of Pittsburgh

and

Myrna Holtz Wooders
Department of Economics
University of Toronto

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 their 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 in the states so that all members of a state are mutually dependent upon each other and no state can credibly threaten to secede. We show that the commonwealth core is equivalent to the partnered core -- when secession is constrained to be carried out only by partnerships the two concepts coincide.