Analytical Stackelberg Resource Allocation in Sequential Attacker--Defender Games

2025-12-19

AI Summary

This paper addresses sequential defense-attack interactions under resource constraints and probabilistic attacks across multiple assets. Method: We formulate an analytical Stackelberg game model wherein the defender commits to a resource allocation strategy first, and the attacker responds optimally given this commitment. Our approach integrates backward induction, probabilistic strategy optimization, and feasibility constraint analysis. Contribution/Results: We derive, for the first time, closed-form equilibrium solutions for both defense and attack strategies in multi-asset, multi-resource settings. We rigorously characterize three distinct regimes of defender payoff and identify the unique Pareto-dominant attack configuration. The equilibrium expressions are general and validated on an eight-asset numerical example, demonstrating clear strategic structure, computational efficiency, and guaranteed feasibility of attack probability distributions. Furthermore, we uncover a phase-transition behavior in defender payoff as defense resources vary.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Adversarial Agents
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

We develop an analytical Stackelberg game framework for optimal resource allocation in a sequential attacker--defender setting with a finite set of assets and probabilistic attacks. The defender commits to a mixed protection strategy, after which the attacker best-responds via backward induction. Closed-form expressions for equilibrium protection and attack strategies are derived for general numbers of assets and defensive resources. Necessary constraints on rewards and costs are established to ensure feasibility of the probability distributions. Three distinct payoff regimes for the defender are identified and analysed. An eight-asset numerical example illustrates the equilibrium structure and reveals a unique Pareto-dominant attack configuration.

Problem

• Develops a Stackelberg game framework for optimal resource allocation in attacker-defender scenarios
• Derives closed-form equilibrium strategies for protection and attack with finite assets
• Identifies and analyzes three distinct payoff regimes for the defender

Innovation

• Analytical Stackelberg game framework for resource allocation
• Closed-form equilibrium strategies derived for multiple assets
• Identified and analysed three distinct defender payoff regimes