TY - GEN
T1 - The cost of stability in weighted voting games
AU - Bachrach, Yoram
AU - Meir, Reshef
AU - Zuckerman, Michael
AU - Rothe, Jörg
AU - Rosenschein, Jeffrey S.
PY - 2009
Y1 - 2009
N2 - One key question in cooperative game theory is that of coalitional stability. A coalition in such games is stable when no subset of the agents in it has a rational incentive to leave the coalition. Finding a division of the gains of the coalition (an imputation) lies at the heart of many cooperative game theory solution concepts, the most prominent of which is the core. However, some coalitional games have empty cores, and any imputation in such a game is unstable. We investigate the possibility of stabilizing the coalitional structure using external payments. In this case, a supplemental payment is offered to the grand coalition by an external party which is interested in having the members of the coalition work together. The sum of this payment plus the gains of the coalition, called the coalition's "adjusted gains", may be divided among the members of the coalition in a stable manner. We call a division of the adjusted gains a super- imputation, and define the cost of stability (CoS) as the minimal sum of payments that stabilizes the coalition. We examine the cost of stability in weighted voting games, where each agent has a weight, and a coalition is successful if the sum of its weights exceeds a given threshold. Such games offer a simple model of decision making in political bodies, and of cooperation in multiagent settings. We show that it is coNP-complcte to test whether a super-imputation is stable, but show that if either the weights or payments of agents are bounded then there exists a polynomial algorithm for this problem. We provide a polynomial approximation algorithm for computing the cost of stability.
AB - One key question in cooperative game theory is that of coalitional stability. A coalition in such games is stable when no subset of the agents in it has a rational incentive to leave the coalition. Finding a division of the gains of the coalition (an imputation) lies at the heart of many cooperative game theory solution concepts, the most prominent of which is the core. However, some coalitional games have empty cores, and any imputation in such a game is unstable. We investigate the possibility of stabilizing the coalitional structure using external payments. In this case, a supplemental payment is offered to the grand coalition by an external party which is interested in having the members of the coalition work together. The sum of this payment plus the gains of the coalition, called the coalition's "adjusted gains", may be divided among the members of the coalition in a stable manner. We call a division of the adjusted gains a super- imputation, and define the cost of stability (CoS) as the minimal sum of payments that stabilizes the coalition. We examine the cost of stability in weighted voting games, where each agent has a weight, and a coalition is successful if the sum of its weights exceeds a given threshold. Such games offer a simple model of decision making in political bodies, and of cooperation in multiagent settings. We show that it is coNP-complcte to test whether a super-imputation is stable, but show that if either the weights or payments of agents are bounded then there exists a polynomial algorithm for this problem. We provide a polynomial approximation algorithm for computing the cost of stability.
KW - Coalition formation
KW - Core
KW - Weighted voting games
UR - http://www.scopus.com/inward/record.url?scp=84899885551&partnerID=8YFLogxK
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AN - SCOPUS:84899885551
SN - 9781615673346
T3 - Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
SP - 1092
EP - 1093
BT - 8th International Joint Conference on Autonomous Agents and Multiagent Systems 2009, AAMAS 2009
PB - International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
T2 - 8th International Joint Conference on Autonomous Agents and Multiagent Systems 2009, AAMAS 2009
Y2 - 10 May 2009 through 15 May 2009
ER -