The cost of stability in coalitional games

Yoram Bachrach*, Edith Elkind, Reshef Meir, Dmitrii Pasechnik, Michael Zuckerman, Jörg Rothe, Jeffrey S. Rosenschein

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

69 Scopus citations

Abstract

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.

Original languageAmerican English
Title of host publicationAlgorithmic Game Theory - Second International Symposium, SAGT 2009, Proceedings
Pages122-134
Number of pages13
DOIs
StatePublished - 2009
Event2nd International Symposium on Algorithmic Game Theory, SAGT 2009 - Paphos, Cyprus
Duration: 18 Oct 200920 Oct 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5814 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference2nd International Symposium on Algorithmic Game Theory, SAGT 2009
Country/TerritoryCyprus
CityPaphos
Period18/10/0920/10/09

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