Bargaining Dynamics in Exchange Networks

TL;DR

This paper analyzes the convergence rate of a dynamical system for Nash bargaining solutions on graphs, showing quadratic convergence times for key elementary structures.

Contribution

It fully characterizes the convergence behavior of the edge-balanced dynamical system for important graph classes, revealing linearity and quadratic convergence times.

Findings

Convergence times are quadratic in the number of matched edges.

Dynamical systems are either linear or become linear over time.

Provides explicit convergence analysis for elementary graph structures.

Abstract

We consider a dynamical system for computing Nash bargaining solutions on graphs and focus on its rate of convergence. More precisely, we analyze the edge-balanced dynamical system by Azar et al and fully specify its convergence for an important class of elementary graph structures that arise in Kleinberg and Tardos' procedure for computing a Nash bargaining solution on general graphs. We show that all these dynamical systems are either linear or eventually become linear and that their convergence times are quadratic in the number of matched edges.