The cost of stability in network flow games

Ezra Resnick*, Yoram Bachrach, Reshef Meir, Jeffrey S. Rosenschein

*Corresponding author for this work

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

24 Scopus citations


The core of a cooperative game contains all stable distributions of a coalition's gains among its members. However, some games have an empty core, with every distribution being unstable. We allow an external party to offer a supplemental payment to the grand coalition, which may stabilize the game, if the payment is sufficiently high. We consider the cost of stability (CoS)-the minimal payment that stabilizes the game. We examine the CoS in threshold network flow games (TNFGs), where each agent controls an edge in a flow network, and a coalition wins if the maximal flow it can achieve exceeds a certain threshold. We show that in such games, it is coNP-complete to determine whether a given distribution (which includes an external payment) is stable. Nevertheless, we show how to bound and approximate the CoS in general TNFGs, and provide efficient algorithms for computing the CoS in several restricted cases.

Original languageAmerican English
Title of host publicationMathematical Foundations of Computer Science 2009 - 34th International Symposium, MFCS 2009, Proceedings
Number of pages15
StatePublished - 2009
Event34th International Symposium on Mathematical Foundations of Computer Science 2009, MFCS 2009 - Novy Smokovec, High Tatras, Slovakia
Duration: 24 Aug 200928 Aug 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5734 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference34th International Symposium on Mathematical Foundations of Computer Science 2009, MFCS 2009
CityNovy Smokovec, High Tatras


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