Nation, J.B.Mizuno, Ryo2013-02-062013-02-062010http://hdl.handle.net/10125/25921Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2010We consider a situation where coalitions are formed to divide a resource. As in real life, the value of a payoff to a given agent is allowed to depend on the payoff to other agents with whom he shares a common interest. There are various notions of equilibrium for this type of game, including the core and no-treat equilibrium. These stabilities may exist or not, depending on the power structure and the rule for allocating the resource. It is shown that under certain conditions, the no-treat equilibrium can exist even though the core is empty.18 pagesAll UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner.Master's project