# A Differential Game Approach to Decentralized Virus-Resistant Weight Adaptation Policy over Complex Networks

## TL;DR

This paper models virus spread in complex networks using a differential game framework, proposing a decentralized weight adaptation policy to mitigate malware propagation and improve network resilience.

## Contribution

It introduces a novel differential game approach for decentralized virus mitigation and designs a penalty-based mechanism to align individual actions with social welfare.

## Key findings

- Nash equilibrium structure characterized in the epidemic control game.
- Decentralized weight adaptation reduces virus spread effectively.
- Penalty scheme improves overall network resilience.

## Abstract

Increasing connectivity of communication networks enables large-scale distributed processing over networks and improves the efficiency for information exchange. However, malware and virus can take advantage of the high connectivity to spread over the network and take control of devices and servers for illicit purposes. In this paper, we use an SIS epidemic model to capture the virus spreading process and develop a virus-resistant weight adaptation scheme to mitigate the spreading over the network. We propose a differential game framework to provide a theoretic underpinning for decentralized mitigation in which nodes of the network cannot fully coordinate, and each node determines its own control policy based on local interactions with neighboring nodes. We characterize and examine the structure of the Nash equilibrium, and discuss the inefficiency of the Nash equilibrium in terms of minimizing the total cost of the whole network. A mechanism design through a penalty scheme is proposed to reduce the inefficiency of the Nash equilibrium and allow the decentralized policy to achieve social welfare for the whole network. We corroborate our results using numerical experiments and show that virus-resistance can be achieved by a distributed weight adaptation scheme.