An axiomatization of the nucleolus
International Journal of Game Theory
An algorithm for finding the nucleolus of assignment games
International Journal of Game Theory
The nucleolus for cooperative games with arbitrary bounds of individual rationality
International Journal of Game Theory
Axiomatization of the nucleolus
Mathematics of Operations Research
The kernel/nucleolus of a standard tree game
International Journal of Game Theory
The nucleon of cooperative games and an algorithm for matching games
Mathematical Programming: Series A and B
Computing the nucleolus of min-cost spanning tree games is NP-hard
International Journal of Game Theory
Applications of approximation algorithms to cooperative games
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On the computation of the nucleolus of a cooperative game
International Journal of Game Theory
On the core of the multicommodity flow game
Proceedings of the 4th ACM conference on Electronic commerce
Complexity of determining nonemptiness of the core
Proceedings of the 4th ACM conference on Electronic commerce
Matching games: the least core and the nucleolus
Mathematics of Operations Research
Limitations of cross-monotonic cost sharing schemes
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Finding nucleolus of flow game
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Settling the Complexity of Two-Player Nash Equilibrium
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Computing Nash Equilibria: Approximation and Smoothed Complexity
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Balanced outcomes in social exchange networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On oblivious PTAS's for nash equilibrium
Proceedings of the forty-first annual ACM symposium on Theory of computing
Network bargaining: algorithms and structural results
Proceedings of the 10th ACM conference on Electronic commerce
An LP approach to compute the pre-kernel for cooperative games
Computers and Operations Research
Convergence of Local Dynamics to Balanced Outcomes in Exchange Networks
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
New algorithms for approximate Nash equilibria in bimatrix games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
An optimization approach for approximate Nash equilibria
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Monotonicity in bargaining networks
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A note on approximate nash equilibria
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Efficient algorithms for constant well supported approximate equilibria in bimatrix games
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
An FPTAS for bargaining networks with unequal bargaining powers
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Fast convergence of natural bargaining dynamics in exchange networks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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
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We study bargaining games between suppliers and manufacturers in a network context. Agents wish to enter into contracts in order to generate surplus which then must be divided among the participants. Potential contracts and their surplus are represented by weighted edges in our bipartite network. Each agent in the market is additionally limited by a capacity representing the number of contracts which he or she may undertake. When all agents are limited to just one contract each, prior research applied natural generalizations of the Nash bargaining solution to the networked setting, defined the new solution concepts of stable and balanced, and characterized the resulting bargaining outcomes. We simplify and generalize these results to a setting in which participants in only one side of the market are limited to one contract each. The core of our results uses a linear-programming formulation to establish a novel connection between well-studied cooperative game theory concepts and the solution concepts of core and prekernel defined for the bargaining games. This immediately implies one can take advantage of the results and algorithms in cooperative game theory to reproduce results such as those of Azar et al. [1] and Kleinberg and Tardos [28] and generalize them to our setting. The cooperative-game-theoretic connection also inspires us to refine our solution space using standard solution concepts from that literature such as nucleolus and lexicographic kernel. The nucleolus is particularly attractive as it is unique, always exists, and is supported by experimental data in the network bargaining literature. Guided by algorithms from cooperative game theory, we show how to compute the nucleolus by pruning and iteratively solving a natural linear-programming formulation.