Infection Spreading and Source Identification: A Hide and Seek Game

TL;DR

This paper models infection spreading and source identification as a strategic game, designing optimal strategies for both players and analyzing conditions for equilibrium, with simulations showing improved infection spread while maintaining source privacy.

Contribution

It introduces a game-theoretic framework for infection source hiding and detection, deriving strategies and equilibrium conditions for both players.

Findings

The infection source can maximize spread while remaining hidden.

The Jordan center estimator is robust against strategic infection strategies.

Simulations confirm the effectiveness of the proposed strategies.

Abstract

The goal of an infection source node (e.g., a rumor or computer virus source) in a network is to spread its infection to as many nodes as possible, while remaining hidden from the network administrator. On the other hand, the network administrator aims to identify the source node based on knowledge of which nodes have been infected. We model the infection spreading and source identification problem as a strategic game, where the infection source and the network administrator are the two players. As the Jordan center estimator is a minimax source estimator that has been shown to be robust in recent works, we assume that the network administrator utilizes a source estimation strategy that can probe any nodes within a given radius of the Jordan center. Given any estimation strategy, we design a best-response infection strategy for the source. Given any infection strategy, we design a best-response estimation strategy for the network administrator. We derive conditions under which a Nash equilibrium of the strategic game exists. Simulations in both synthetic and real-world networks demonstrate that our proposed infection strategy infects more nodes while maintaining the same safety margin between the true source node and the Jordan center source estimator.