Distributed linear programming and bargaining in exchange networks

Many engineering, economic, and social scenarios are modeled as neighboring agents in a network interacting with each other. In the setup we consider, neighboring agents (i) bargain over the possibility of matching with at most one other agent and (ii) agree on how to allocate a common good between them. In particular, we examine stable and fair outcomes called Nash bargaining solutions. Our main contribution is the design of continuous-time distributed dynamics that converge to these Nash solutions. The technical approach leads us to develop distributed dynamics for linear programming, the results of which are of independent interest. We invoke Lyapunov techniques to prove convergence and draw results from nonsmooth and set-valued analysis of dynamical systems. In the literature pertinent to bargaining problems of the form we consider, this control perspective is unique.