Analytical Stackelberg Resource Allocation in Sequential Attacker--Defender Games

TL;DR

This paper introduces an analytical Stackelberg game model for optimal sequential resource allocation in attacker-defender scenarios, deriving closed-form equilibrium strategies and analyzing different payoff regimes.

Contribution

It provides a novel analytical framework with closed-form solutions for equilibrium strategies in sequential attacker-defender games with multiple assets.

Findings

Closed-form equilibrium strategies derived for general asset numbers.

Identification of three distinct defender payoff regimes.

Numerical example with eight assets illustrating equilibrium and attack configurations.

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.