The auction algorithm: a distributed relaxation method for the assignment problem
Annals of Operations Research - Special Issue: Parallel Optimization on Novel Computer Architectures
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
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
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
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
Belief propagation for min-cost network flow: convergence & correctness
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
An FPTAS for bargaining networks with unequal bargaining powers
WINE'10 Proceedings of the 6th international conference on Internet and network economics
MAP estimation via agreement on trees: message-passing and linear programming
IEEE Transactions on Information Theory
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
Belief Propagation for Min-Cost Network Flow: Convergence and Correctness
Operations Research
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
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Bargaining networks model the behavior of a set of players who need to reach pairwise agreements for making profits. Nash bargaining solutions in this context correspond to solutions which are stable and balanced. Kleinberg and Tardos [19] proved that, if such solutions exist, then they can by calculated in polynomial time. This left open the question: Are there dynamics which can describe the bargaining process of real-world players, and which converge quickly to a Nash bargaining solution? This paper provides an affirmative answer to that question. The contribution of this paper is threefold: (1) We introduce a single-stage local dynamics which models the way in which actual players could bargain. We show that (approximate) fixed points of our dynamics are in one-to-one correspondence with (approximate) Nash bargaining solutions. (2) We prove that our dynamics converges to an ε-fixed point in O(1/ε2) iterations independent of the network size when the potential earnings (weights) are uniformly bounded. We use this to prove that an approximate Nash bargaining solution is reached in time polynomial in 1/ε, the network size and 1/g. Here g is the difference between the weights of the two corners of the matching polytope having largest weights, and controls the behavior of fast message passing algorithms for maximum weight matching (matching naturally arises as a subproblem of Nash bargaining). (3) Our proof introduces a new powerful technique from functional analysis to this set of problems. The technique allows us to extend our results in various directions. We believe the tools introduced here will be useful in many related problems. As a corollary, for bipartite graphs we prove polynomial time convergence to an approximate Nash bargaining solution, with probability close to one under small random perturbations.