Theory of linear and integer programming
Theory of linear and integer programming
Algorithmic Aspects of the Core of Combinatorial Optimization Games
Mathematics of Operations Research
Balanced outcomes in social exchange networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
The cooperative game theory foundations of network bargaining games
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Iterative Methods in Combinatorial Optimization
Iterative Methods in Combinatorial Optimization
Computational Aspects of Cooperative Game Theory (Synthesis Lectures on Artificial Inetlligence and Machine Learning)
On solution concepts for matching games
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
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We study a network extension to the Nash bargaining game, as introduced by Kleinberg and Tardos [6], where the set of players corresponds to vertices in a graph G=(V,E) and each edge ij∈E represents a possible deal between players i and j. We reformulate the problem as a cooperative game and study the following question: Given a game with an empty core (i.e. an unstable game) is it possible, through minimal changes in the underlying network, to stabilize the game? We show that by removing edges in the network that belong to a blocking set we can find a stable solution in polynomial time. This motivates the problem of finding small blocking sets. While it has been previously shown that finding the smallest blocking set is NP-hard [2], we show that it is possible to efficiently find approximate blocking sets in sparse graphs.