Analytical Stackelberg Resource Allocation in Sequential Attacker--Defender Games

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.

💡 Research Summary

The paper presents a rigorous Stackelberg game model for optimal resource allocation in a sequential attacker‑defender setting. The defender (leader) first commits to a mixed protection strategy over a finite set of assets, and the attacker (follower) observes this commitment and then chooses a mixed attack strategy that maximizes its expected payoff. The authors derive closed‑form expressions for the equilibrium strategies that hold for any numbers of assets (N) and defensive resources (M).

Key modeling steps:

1. Protection probabilities – Each asset (T_n) can be protected by any of the (M) resources (S_m). The joint probability (Pr(T_n,S_m)) is defined, and the marginal protection probability for asset (n) is (D_n = \frac{1}{M}\sum_{m=1}^{M}Pr(T_n,S_m)). Normalization requires that for each resource the sum of its allocation probabilities across all assets equals one.
2. Reward‑cost structure – For each asset the defender receives reward (R_B(T_n)) if it is protected and incurs cost (C_B(T_n)) if it is unprotected. Conversely, the attacker receives reward (R_R(T_n)) when an unprotected asset is hit and pays cost (C_R(T_n)) when the asset is defended. Expected payoffs are
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