The cost of stability in coalitional games
Pasechnik, Dmitrii V.
Rosenschein, Jeffrey S.
Date of Issue2009
Symposium on Algorithmic Game Theory (2nd : 2009 : Paphos, Cyprus)
School of Physical and Mathematical Sciences
A key question in cooperative game theory is that of coalitional stability, usually captured by the notion of the core--the set of outcomes such that no subgroup of players has an incentive to deviate. However, some coalitional games have empty cores, and any outcome in such a game is unstable. In this paper, we investigate the possibility of stabilizing a coalitional game by using external payments. We consider a scenario where an external party, which is interested in having the players work together, offers a supplemental payment to the grand coalition (or, more generally, a particular coalition structure). This payment is conditional on players not deviating from their coalition(s). The sum of this payment plus the actual gains of the coalition(s) may then be divided among the agents so as to promote stability. We define the cost of stability (CoS) as the minimal external payment that stabilizes the game. We provide general bounds on the cost of stability in several classes of games, and explore its algorithmic properties. To develop a better intuition for the concepts we introduce, we provide a detailed algorithmic study of the cost of stability in weighted voting games, a simple but expressive class of games which can model decision-making in political bodies, and cooperation in multiagent settings. Finally, we extend our model and results to games with coalition structures.
© 2009 Springer-Verlag Berlin Heidelberg. This is the author created version of a work that has been peer reviewed and accepted for publication by Proceedings of SAGT 2009, LNCS 5814, Springer-Verlag Berlin Heidelberg. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [DOI: http://dx.doi.org/10.1007/978-3-642-04645-2 ].