Zero-determinant Strategy for Moving Target Defense: Existence, Performance, and Computation

2026-05-08

AI Summary

This work addresses the high computational complexity of traditional strong Stackelberg equilibria (SSE) in multi-objective dynamic defense, which limits their practical applicability. For the first time, zero-determinant (ZD) strategies are introduced into this setting, and the necessary and sufficient conditions for their existence are rigorously established. Theoretical analysis demonstrates that the performance upper bound of ZD strategies can attain the level of SSE. By formulating the interaction as a game-theoretic model, analyzing ZD strategy properties, and designing an efficient optimization algorithm, the proposed approach substantially reduces computational overhead. Experimental evaluations in two realistic defense scenarios confirm that the method achieves defense effectiveness comparable to SSE while significantly improving computational efficiency.

Abstract

Moving Target Defense (MTD) is commonly formulated as a repeated security game to mitigate persistent threats. Although the strong Stackelberg equilibrium (SSE) characterizes the defender's optimal strategy in the leader-follower framework, computing the SSE often incurs high computational complexity, which significantly limits its practical deployment in MTD problems with multiple targets. This paper proposes adopting a zero-determinant (ZD) strategy for constructing an MTD strategy that achieves both high defensive performance and substantially low computational complexity. We first derive a necessary and sufficient condition for the existence of ZD strategies and investigate the performance of ZD strategies, which shows their upper-bound performance matches that of the SSE strategy. We then formulate two programs to find the optimal ZD strategy parameters under different conditions. Moreover, we design an algorithm to compute the proposed ZD strategies, along with the computational complexity analysis in comparison with the traditional SSE computation. Finally, we conduct experiments on two practical applications to verify our results.

Problem

• Moving Target Defense
• Stackelberg equilibrium
• computational complexity
• security game
• zero-determinant strategy

Innovation

• Zero-Determinant Strategy
• Moving Target Defense
• Stackelberg Equilibrium
• Computational Complexity
• Security Game