Bargaining Solutions in a Social Network
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Network bargaining: algorithms and structural results
Proceedings of the 10th ACM conference on Electronic commerce
A behavioral study of bargaining in social networks
Proceedings of the 11th ACM conference on Electronic commerce
Monotonicity in bargaining networks
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
The cooperative game theory foundations of network bargaining games
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Contribution games in social networks
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Local dynamics in bargaining networks via random-turn games
WINE'10 Proceedings of the 6th international conference on Internet and network economics
An FPTAS for bargaining networks with unequal bargaining powers
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Game theoretic models for social network analysis
Proceedings of the 20th international conference companion on World wide web
Fast convergence of natural bargaining dynamics in exchange networks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Multiagent task allocation in social networks
Autonomous Agents and Multi-Agent Systems
Searching Steiner trees for web graph query
Computers and Industrial Engineering
Ranking structural parameters for social networks
DASFAA'12 Proceedings of the 17th international conference on Database Systems for Advanced Applications
Optimizing social welfare for network bargaining games in the face of unstability, greed and spite
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Network bargaining: using approximate blocking sets to stabilize unstable instances
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
Bargaining for revenue shares on tree trading networks
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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The study of bargaining has a long history, but many basic settings are still rich with unresolved questions. In particular, consider a set of agents who engage in bargaining with one another,but instead of pairs of agents interacting in isolation,agents have the opportunity to choose whom they want to negotiate with, along the edges of a graph representing social-network relations. The area of network exchange theory in sociology has developed a large body of experimental evidence for the way in which people behave in such network-constrained bargaining situations, and it is a challenging problem to develop models that are both mathematically tractable and in general agreement with the results of these experiments. We analyze a natural theoretical model arising in network exchange theory, which can be viewed as a direct extension of the well-known Nash bargaining solution to the case of multiple agents interacting on a graph. While this generalized Nash bargaining solution is surprisingly effective at picking up even subtle differences in bargaining power that have been observed experimentally on small examples, it has remained an open question to characterize the values taken by this solution on general graphs, or to find an efficient means to compute it. Here we resolve these questions, characterizing the possible values of this bargaining solution, and giving an efficient algorithm to compute the set of possible values. Our result exploits connections to the structure of matchings in graphs, including decomposition theorems for graphs with perfect matchings, and also involves the development of new techniques. In particular, the values we are seeking turn out to correspond to a novel combinatorially defined point in the interior of a fractional relaxation of the matching problem.