Fast Convergence of Natural Bargaining Dynamics in Exchange Networks

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 -fixed point in O(1/2 ) iterations independent of the network size when the potential earnings (weights) are...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Yashodhan Kanoria, Mohsen Bayati, Christian Borgs, Jennifer T. Chayes, Andrea Montanari
• Keywords: Bargaining, CORR 2010, Education, Polynomial Time, Solution