Dynamic Resilient Network Games with Applications to Multi-Agent Consensus

TL;DR

This paper models a cyber security scenario as a two-player game on networks, analyzing how attacks and defenses impact network connectivity and multi-agent consensus, with strategies constrained by energy limits.

Contribution

It introduces a novel game-theoretic framework for resilient network defense and applies it to multi-agent consensus, characterizing optimal strategies under energy constraints.

Findings

Optimal attack and defense strategies depend on edge connectivity.

Edge removals and recoveries significantly influence consensus dynamics.

Numerical simulations validate the theoretical results.

Abstract

A cyber security problem in a networked system formulated as a resilient graph problem based on a game-theoretic approach is considered. The connectivity of the underlying graph of the network system is reduced by an attacker who removes some of the edges whereas the defender attempts to recover them. Both players are subject to energy constraints so that their actions are restricted and cannot be performed continuously. For this two-stage game, which is played repeatedly over time, we characterize the optimal strategies for the attacker and the defender in terms of edge connectivity and the number of connected components of the graph. The resilient graph game is then applied to a multi-agent consensus problem. We study how the attacks and the recovery on the edges affect the consensus process. Finally, we also provide numerical simulation to illustrate the results.