Consensus over evolutionary graphs

TL;DR

This paper proves that a group of strategic agents with private rewards can reach average consensus over dynamic, evolving networks driven by their own link-creation and deletion decisions, despite the complexity of the changing topology.

Contribution

It introduces a novel model where agents control network links based on selfish decisions, and proves consensus results for such evolving, state-dependent graphs.

Findings

Almost sure and mean square consensus achieved

Exponential convergence in expectation proven

Validated through simulation on random networks

Abstract

We establish average consensus on graphs with dynamic topologies prescribed by evolutionary games among strategic agents. Each agent possesses a private reward function and dynamically decides whether to create new links and/or whether to delete existing ones in a selfish and decentralized fashion, as indicated by a certain randomized mechanism. This model incurs a time-varying and state-dependent graph topology for which traditional consensus analysis is not applicable. We prove asymptotic average consensus almost surely and in mean square for any initial condition and graph topology. In addition, we establish exponential convergence in expectation. Our results are validated via simulation studies on random networks.