Convergence of Local Dynamics to Balanced Outcomes in Exchange Networks

TL;DR

This paper investigates local dynamics in exchange networks, demonstrating that simple edge-balancing processes converge efficiently to balanced outcomes, which are key for stability and fairness in bargaining games.

Contribution

It introduces and proves convergence of simple local edge-balancing dynamics to balanced outcomes in exchange networks.

Findings

Edge-balancing dynamics converge to balanced outcomes when they exist.

The convergence occurs in polynomial time.

The work bridges local process dynamics with global equilibrium concepts.

Abstract

Bargaining games on exchange networks have been studied by both economists and sociologists. A Balanced Outcome for such a game is an equilibrium concept that combines notions of stability and fairness. In a recent paper, Kleinberg and Tardos introduced balanced outcomes to the computer science community and provided a polynomial-time algorithm to compute the set of such outcomes. Their work left open a pertinent question: are there natural, local dynamics that converge quickly to a balanced outcome? In this paper, we provide a partial answer to this question by showing that simple edge-balancing dynamics converge to a balanced outcome whenever one exists.