Deception Equilibrium Analysis for Three-Party Stackelberg Game with Insider

2026-04-03

AI Summary

This work addresses the degradation of defensive efficacy in triadic security games involving defenders, insiders, and external attackers, which arises from information misperception and uncertainty. To counter this, the paper proposes a unified leader-follower deception game framework that achieves robust deception by strategically manipulating the follower’s perceived parameters. It innovatively introduces the concepts of Deceptive Stackelberg Equilibrium (DSE) and Hyper-Nash Equilibrium (HNE), establishes their consistency conditions, and designs a scalable hypergradient algorithm to compute equilibria under nonsmooth, set-valued best-response mappings. Through rigorous game-theoretic modeling and convergence analysis, the approach is validated in two practical scenarios—secure wireless communications and defense against insider-assisted false data injection attacks—demonstrating its effectiveness in enabling efficient and scalable computation of deceptive equilibria.

Abstract

This paper investigates strategic interactions within a three party deception security game involving a defender, an insider, and external attackers. We propose a robust deception mechanism where the leader manipulates game parameters perceived by followers to enhance defense performance when followers operate under misperceived and uncertain observation. Specifically, we propose a unified three party leader follower game framework and introduce the concepts of Deception Stackelberg equilibria (DSE) and Hyper Nash equilibria (HNE), which generalize classical two-player Stackelberg and deception games. We develop necessary and sufficient conditions for the consistency between DSE and HNE, ensuring that the defender's utility remains invariant when the hierarchical structure degenerates into a simultaneous-move scenario. Moreover, we propose a scalable hypergradient-based algorithm with established convergence guarantees for seeking DSE, efficiently addressing the computational challenges posed by non-smooth and set-valued best-response mappings. Finally, we apply theoretical analysis to practical scenarios in secure wireless communication and defense against insider-assisted false data injection attacks.

Problem

• deception
• Stackelberg game
• insider threat
• security game
• equilibrium

Innovation

• Deception Stackelberg Equilibrium
• Hyper Nash Equilibrium
• Three-party Stackelberg Game
• Hypergradient Algorithm
• Insider Threat