Distributed bargaining in dyadic-exchange networks

TL;DR

This paper develops distributed continuous-time algorithms for agents in dyadic-exchange networks to autonomously find stable, balanced, and Nash outcomes, with applications demonstrated in wireless communication systems.

Contribution

It introduces provably-correct algorithms for computing various bargaining solutions in a distributed manner, integrating stability and fairness considerations.

Findings

Algorithms converge to desired outcomes

Framework applicable to wireless communication scenarios

Robustness established through theoretical analysis

Abstract

This paper considers dyadic-exchange networks in which individual agents autonomously form coalitions of size two and agree on how to split a transferable utility. Valid results for this game include stable (if agents have no unilateral incentive to deviate), balanced (if matched agents obtain similar benefits from collaborating), or Nash (both stable and balanced) outcomes. We design provably-correct continuous-time algorithms to find each of these classes of outcomes in a distributed way. Our algorithmic design to find Nash bargaining solutions builds on the other two algorithms by having the dynamics for finding stable outcomes feeding into the one for finding balanced ones. Our technical approach to establish convergence and robustness combines notions and tools from optimization, graph theory, nonsmooth analysis, and Lyapunov stability theory and provides a useful framework for further extensions. We illustrate our results in a wireless communication scenario where single-antenna devices have the possibility of working as 2-antenna virtual devices to improve channel capacity.