[Paper Review] Colonel Blotto Game for Secure State Estimation in Interdependent Critical Infrastructure

Aidin Ferdowsi, Walid Saad+1 more|arXiv (Cornell University)|Sep 27, 2017

Smart Grid Security and Resilience19 citations

TL;DR

This paper proposes a Colonel Blotto game framework to model strategic interactions between an attacker compromising sensors and a defender allocating limited protection resources in interdependent critical infrastructures (ICIs). By deriving a mixed-strategy Nash equilibrium, the defender can randomize sensor protection levels to reduce state estimation error by at least 50% compared to non-strategic allocation.

ABSTRACT

Securing the physical components of a city's interdependent critical infrastructure (ICI) such as power, natural gas, and water systems is a challenging task due to their interdependence and a large number of involved sensors. In this paper, using a novel integrated state-space model that captures the interdependence, a two-stage cyber attack on an ICI is studied in which the attacker first compromises the ICI's sensors by decoding their messages, and, subsequently, it alters the compromised sensors' data to cause state estimation errors. To thwart such attacks, the administrator of each critical infrastructure (CI) must assign protection levels to the sensors based on their importance in the state estimation process. To capture the interdependence between the attacker and the ICI administrator's actions and analyze their interactions, a Colonel Blotto game framework is proposed. The mixed-strategy Nash equilibrium of this game is derived analytically. At this equilibrium, it is shown that the administrator can strategically randomize between the protection levels of the sensors to deceive the attacker. Simulation results coupled with theoretical analysis show that, using the proposed game, the administrator can reduce the state estimation error by at least $ 50\\% $ compared to a non-strategic approach that assigns protection levels proportional to sensor values.

Motivation & Objective

• Address the challenge of securing interdependent critical infrastructures (ICIs) with limited security resources and sensor-level cyber-physical attacks.
• Model the strategic interaction between an attacker targeting sensors and a defender allocating protection resources as a Colonel Blotto game.
• Develop a game-theoretic framework that accounts for interdependencies among power, gas, and water systems in state estimation.
• Provide a mixed-strategy Nash equilibrium solution that enables the defender to deceive the attacker through randomized protection allocation.
• Demonstrate that strategic protection allocation significantly reduces state estimation error compared to value-proportional, non-strategic approaches.

Proposed method

• Formulate a unified state-space model for interdependent power, gas, and water infrastructures using coupled dynamics with interdependency matrices.
• Model the two-stage attack: sensor compromise via message decoding, followed by data injection to induce estimation errors.
• Define the defender’s strategy as allocating limited protection resources across sensors based on their importance in state estimation.
• Construct a Colonel Blotto game where the attacker and defender allocate resources across sensor battlefields, with the defender’s goal to minimize estimation error.
• Derive the mixed-strategy Nash equilibrium analytically, enabling the defender to randomize protection levels and deceive the attacker.
• Integrate the game-theoretic solution into a Kalman filter-based state estimation framework to evaluate performance under attack.

Experimental results

Research questions

• RQ1 How can the defender optimally allocate limited protection resources across sensors in interdependent critical infrastructures to minimize state estimation error?
• RQ2 What is the impact of interdependencies between power, gas, and water systems on the strategic allocation of security resources?
• RQ3 How does a mixed-strategy Colonel Blotto game equilibrium improve security compared to non-strategic, value-proportional protection allocation?
• RQ4 To what extent can strategic randomization in protection levels deceive an intelligent attacker in a two-stage sensor compromise attack?
• RQ5 What is the quantitative reduction in state estimation error achieved by using the proposed game-theoretic defense strategy?

Key findings

• The proposed Colonel Blotto game framework enables the defender to achieve a mixed-strategy Nash equilibrium that strategically randomizes sensor protection levels.
• The defender’s equilibrium strategy effectively deceives the attacker by making it difficult to predict high-value targets, reducing the attacker’s success rate.
• Simulation and theoretical analysis show that the proposed method reduces state estimation error by at least 50% compared to non-strategic, value-proportional protection allocation.
• The interdependency model captures cross-system dynamics, showing that failures or attacks in one infrastructure can propagate and degrade performance in others.
• The game-theoretic approach outperforms traditional, non-strategic defense mechanisms by explicitly modeling attacker intent and resource constraints.
• The derived equilibrium ensures robustness against stealthy, two-stage attacks involving sensor compromise and data injection, even under limited defender resources.