A Rolling Horizon Game Considering Network Effect in Cluster Forming for Dynamic Resilient Multiagent Systems

TL;DR

This paper models a dynamic multiagent network as a two-player game where an attacker and defender strategically disable or recover edges, affecting cluster formation and consensus, with strategies optimized over a rolling horizon considering energy constraints.

Contribution

It introduces a novel game-theoretic framework for resilient multiagent systems that accounts for network effects and energy constraints in dynamic cluster formation.

Findings

Optimal strategies depend on energy constraints and network effects.

The number of clusters at equilibrium can be characterized under attack and recovery.

Simulation demonstrates the impact of strategies on cluster dynamics.

Abstract

A two-player game-theoretic problem on resilient graphs in a multiagent consensus setting is formulated. An attacker is capable to disable some of the edges of the network with the objective to divide the agents into clusters by emitting jamming signals while, in response, the defender recovers some of the edges by increasing the transmission power for the communication signals. Specifically, we consider repeated games between the attacker and the defender where the optimal strategies for the two players are derived in a rolling horizon fashion based on utility functions that take both the agents' states and the sizes of clusters (known as network effect) into account. The players' actions at each discrete-time step are constrained by their energy for transmissions of the signals, with a less strict constraint for the attacker. Necessary conditions and sufficient conditions of agent consensus are derived, which are influenced by the energy constraints. The number of clusters of agents at infinite time in the face of attacks and recoveries are also characterized. Simulation results are provided to demonstrate the effects of players' actions on the cluster forming and to illustrate the players' performance for different horizon parameters.