Robust Distributed Averaging on Networks with Adversarial Intervention

TL;DR

This paper analyzes a strategic game between a network designer and an adversary affecting distributed averaging, deriving optimal strategies and conditions for equilibrium using Pontryagin's Maximum Principle.

Contribution

It introduces a game-theoretic framework for adversarial interventions in distributed averaging networks and characterizes optimal strategies and equilibrium conditions.

Findings

Derived optimal strategies using Pontryagin's Maximum Principle

Connected optimal strategies with potential theory

Provided a sufficient condition for saddle-point equilibrium

Abstract

We study the interaction between a network designer and an adversary over a dynamical network. The network consists of nodes performing continuous-time distributed averaging. The goal of the network designer is to assist the nodes reach consensus by changing the weights of a limited number of links in the network. Meanwhile, an adversary strategically disconnects a set of links to prevent the nodes from converging. We formulate two problems to describe this competition where the order in which the players act is reversed in the two problems. We utilize Pontryagin's Maximum Principle (MP) to tackle both problems and derive the optimal strategies. Although the canonical equations provided by the MP are intractable, we provide an alternative characterization for the optimal strategies that highlights a connection with potential theory. Finally, we provide a sufficient condition for the existence of a saddle-point equilibrium (SPE) for this zero-sum game.