Title: Fast Convergence of Natural Dynamics in Bargaining Networks
Time: 3.30 pm, 7/1/11
Venue: Room 217, Mechanical Engg. Building
Abstract: Bargaining networks model the behavior of a set of players that need to reach pairwise agreements for making profits. Players bargain with possible `partners' on how to potentially share the gain from their partnership. Agents are allowed to form at most one partnership each, for example. Nash bargaining solutions are special outcomes of such games that are both stable and balanced. Kleinberg and Tardos proved an algorithmic characterization of such outcomes, but left
open the problem of how the actual bargaining process converges to them.
We introduce a simple and natural model for this process, and show fast convergence to approximate Nash bargaining solutions. Consider an exchange network represented by a weighted graph. At each time step, each player proposes a deal to each of her neighbors. The proposal consists of a share of the potential profit in case of agreement. The share is chosen to be balanced in Nash's sense as far as this is feasible (with respect to the current best alternatives for both players). We show that (approximate) fixed points of our dynamics correspond to (approximate) Nash bargaining solutions when such solutions exist. We also prove that our dynamics converges to an \eps-approximate fixed point in time O(\eps^{-2}) independent of the network size. Moreover, for small enough \eps, the best pairing between the nodes emerges. As an example, we prove that for bipartite graphs this leads to polynomial time convergence to an approximate Nash bargaining solution under a smoothed analysis.
Further, we generalize to the case of unequal bargaining powers: We characterize existence of solutions and provide the first FPTAS for computing them.
Joint work with Mohsen Bayati, Jennifer Chayes, Christian Borgs and Andrea Montanari. Based on papers in SODA 2011 and WINE 2010.
Speaker's Bio: Yashodhan Kanoria obtained a B.Tech. in EE from IIT Bombay in 2007 and is currently a PhD student at Stanford University. He received a Student paper award at the IEEE International Symposium on Information Theory, 2010. His main research interests are social learning and learning in network games.