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"A key question in cooperative game theory is that of coalitional stability,\nusually captured by the notion of the core--the set of outcomes such\nthat no subgroup of players has an incentive to deviate. However, some\ncoalitional games have empty cores, and any outcome in such a game is unstable.\n  In this paper, we investigate the possibility of stabilizing a coalitional\ngame by using external payments. We consider a scenario where an external\nparty, which is interested in having the players work together, offers a\nsupplemental payment to the grand coalition (or, more generally, a particular\ncoalition structure). This payment is conditional on players not deviating from\ntheir coalition(s). The sum of this payment plus the actual gains of the\ncoalition(s) may then be divided among the agents so as to promote stability.\nWe define the cost of stability (CoS) as the minimal external payment\nthat stabilizes the game.\n  We provide general bounds on the cost of stability in several classes of\ngames, and explore its algorithmic properties. To develop a better intuition\nfor the concepts we introduce, we provide a detailed algorithmic study of the\ncost of stability in weighted voting games, a simple but expressive class of\ngames which can model decision-making in political bodies, and cooperation in\nmultiagent settings. Finally, we extend our model and results to games with\ncoalition structures."
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