Faster scaling algorithms for general graph matching problems
Journal of the ACM (JACM)
On the computation of the nucleolus of a cooperative game
International Journal of Game Theory
Balanced outcomes in social exchange networks
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
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
A behavioral study of bargaining in social networks
Proceedings of the 11th ACM conference on Electronic commerce
The cooperative game theory foundations of network bargaining games
ICALP'10 Proceedings of the 37th international colloquium 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
Max-Product for Maximum Weight Matching: Convergence, Correctness, and LP Duality
IEEE Transactions on Information Theory
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
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
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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Bargaining networks model social or economic situations in which agents seek to form the most lucrative partnership with another agent from among several alternatives. There has been a flurry of recent research studying Nash bargaining solutions (also called 'balanced outcomes') in bargaining networks, so that we now know when such solutions exist, and that they can be computed efficiently, even by market agents behaving in a natural manner. In this work we study a generalization of Nash bargaining, that models the possibility of unequal 'bargaining powers'. This generalization was introduced in [12], where it was shown that the corresponding 'unequal division' (UD) solutions exist if and only if Nash bargaining solutions exist, and also that a certain local dynamics converges to UD solutions when they exist. However, the convergence time for that dynamics was exponential in network size for the unequal division case. Other approaches, such as the one of Kleinberg and Tardos, do not generalize to the unsymmetrical case. Thus, the question of computational tractability of UD solutions has remained open. In this paper, we provide an FPTAS for the computation of UD solutions, when such solutions exist. On a graph G = (V,E) with weights (i.e. pairwise profit opportunities) uniformly bounded above by 1, our FPTAS finds an ε-UD solution in time polynomial in the input and 1/ε. We also provide a fast local algorithm for finding ε-UD solution.