Interdependent Defense Games: Modeling Interdependent Security under Deliberate Attacks

TL;DR

This paper introduces interdependent defense (IDD) games, a game-theoretic framework modeling security risks in multi-agent systems under deliberate attacks, providing equilibrium analysis and empirical evaluation on real-world network data.

Contribution

It extends IDS games to model attacker deliberate behavior, characterizes Nash equilibria, and offers a polynomial-time algorithm for their computation, along with a real-world network-based game generator.

Findings

Complete characterization of mixed-strategy Nash equilibria.

Polynomial-time algorithm for computing equilibria in IDD games.

Empirical results on Internet-derived network data using learning heuristics.

Abstract

We propose interdependent defense (IDD) games, a computational game-theoretic framework to study aspects of the interdependence of risk and security in multi-agent systems under deliberate external attacks. Our model builds upon interdependent security (IDS) games, a model due to Heal and Kunreuther that considers the source of the risk to be the result of a fixed randomizedstrategy. We adapt IDS games to model the attacker's deliberate behavior. We define the attacker's pure-strategy space and utility function and derive appropriate cost functions for the defenders. We provide a complete characterization of mixed-strategy Nash equilibria (MSNE), and design a simple polynomial-time algorithm for computing all of them, for an important subclass of IDD games. In addition, we propose a randominstance generator of (general) IDD games based on a version of the real-world Internet-derived Autonomous Systems (AS) graph (with around 27K nodes and 100K edges), and present promising empirical results using a simple learning heuristics to compute (approximate) MSNE in such games.