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Integrating Sequential Hypothesis Testing into Adversarial Games: A Sun Zi-Inspired Framework

Haosheng Zhou, Daniel Ralston, Xu Yang, Ruimeng Hu

TL;DR

This work tackles deception in adversarial decision-making under partial observability by embedding sequential hypothesis testing into a Stackelberg framework. It develops a linear-quadratic model where the blue team balances a primary velocity-control objective with misdirection driven by the SHT likelihood ratio $L_T$, while the red team counters by leveraging leaked patterns to counter deception. A semi-explicit solution for the blue team's controls is derived via a quadratic value function, and a reduced game with regularization clarifies the strategic interaction between deception and skepticism, with numerical experiments validating the framework. By unifying Sun Zi's strategic principles with contemporary control and game theory, the paper highlights deception-aware design opportunities for domains such as cybersecurity, autonomous systems, and financial markets.

Abstract

This paper investigates the interplay between sequential hypothesis testing (SHT) and adversarial decision-making in partially observable games, focusing on the deceptive strategies of red and blue teams. Inspired by Sun Zi's The Art of War and its emphasis on deception, we develop a novel framework to both deceive adversaries and counter their deceptive tactics. We model this interaction as a Stackelberg game where the blue team, as the follower, optimizes its controls to achieve its goals while misleading the red team into forming incorrect beliefs on its intentions. The red team, as the leader, strategically constructs and instills false beliefs through the blue team's envisioned SHT to manipulate the blue team's behavior and reveal its true objectives. The blue team's optimization problem balances the fulfillment of its primary objectives and the level of misdirection, while the red team coaxes the blue team into behaving consistently with its actual intentions. We derive a semi-explicit solution for the blue team's control problem within a linear-quadratic framework, and illustrate how the red team leverages leaked information from the blue team to counteract deception. Numerical experiments validate the model, showcasing the effectiveness of deception-driven strategies in adversarial systems. These findings integrate ancient strategic insights with modern control and game theory, providing a foundation for further exploration in adversarial decision-making, such as cybersecurity, autonomous systems, and financial markets.

Integrating Sequential Hypothesis Testing into Adversarial Games: A Sun Zi-Inspired Framework

TL;DR

This work tackles deception in adversarial decision-making under partial observability by embedding sequential hypothesis testing into a Stackelberg framework. It develops a linear-quadratic model where the blue team balances a primary velocity-control objective with misdirection driven by the SHT likelihood ratio , while the red team counters by leveraging leaked patterns to counter deception. A semi-explicit solution for the blue team's controls is derived via a quadratic value function, and a reduced game with regularization clarifies the strategic interaction between deception and skepticism, with numerical experiments validating the framework. By unifying Sun Zi's strategic principles with contemporary control and game theory, the paper highlights deception-aware design opportunities for domains such as cybersecurity, autonomous systems, and financial markets.

Abstract

This paper investigates the interplay between sequential hypothesis testing (SHT) and adversarial decision-making in partially observable games, focusing on the deceptive strategies of red and blue teams. Inspired by Sun Zi's The Art of War and its emphasis on deception, we develop a novel framework to both deceive adversaries and counter their deceptive tactics. We model this interaction as a Stackelberg game where the blue team, as the follower, optimizes its controls to achieve its goals while misleading the red team into forming incorrect beliefs on its intentions. The red team, as the leader, strategically constructs and instills false beliefs through the blue team's envisioned SHT to manipulate the blue team's behavior and reveal its true objectives. The blue team's optimization problem balances the fulfillment of its primary objectives and the level of misdirection, while the red team coaxes the blue team into behaving consistently with its actual intentions. We derive a semi-explicit solution for the blue team's control problem within a linear-quadratic framework, and illustrate how the red team leverages leaked information from the blue team to counteract deception. Numerical experiments validate the model, showcasing the effectiveness of deception-driven strategies in adversarial systems. These findings integrate ancient strategic insights with modern control and game theory, providing a foundation for further exploration in adversarial decision-making, such as cybersecurity, autonomous systems, and financial markets.

Paper Structure

This paper contains 10 sections, 6 theorems, 23 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The Linear-Quadratic Model
  3. The Primary Task -- a Baseline Model
  4. Intention Inference with SHT in a Partially Observable Environment
  5. Linear-Quadratic Model for Strategic Misdirection
  6. The Stackelberg Game
  7. Numerical Results
  8. Blue Team's Optimal Control $\hat{\beta}_t$
  9. Red Team's Optimal Control $\hat{f}_c$
  10. Conclusions and Future Works

Key Result

Proposition 1

Denote by $\mu^{H_0}_{(V,Y)}$ and $\mu^{H_1}_{(V,Y)}$ the law of $\{V_t,Y_t\}$ under $H_0$ and $H_1$ respectively. Under Assumption assu:linear_ctrl, the SHT statistic is given by: where $(V,Y)$ are random processes that follow the dynamics eqn:velocity--eqn:position under $H_0$.

Figures (3)

  • Figure 1: Comparisons of the optimal trajectories \ref{['eqn:velocity']}--\ref{['eqn:position']} and controls \ref{['eqn:solution']} with $\lambda = 0.075$ across different choices of $f_c$: baseline $f_c\equiv 0$, positive $f_c\equiv 0.5$, negative $f_c\equiv -0.25$, and periodic $f_c(t) = 0.5\sin(10\pi t)$.
  • Figure 2: Comparisons of the optimal trajectories \ref{['eqn:velocity']}--\ref{['eqn:position']} and controls \ref{['eqn:solution']} with $f_c(t) = \sin(10\pi t)$ across different values of $\lambda$.
  • Figure 3: Plots of the optimal $\hat{f}_c$ across different algorithms, penalties, and values of $\lambda_{\text{reg}}$.

Theorems & Definitions (13)

  • Remark 1: Model interpretation
  • Remark 2
  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Theorem 1: Local Existence and Uniqueness
  • proof
  • Lemma 1: jacobson1970new, mrtensson1971matrix
  • Theorem 2: Global Existence and Uniqueness
  • ...and 3 more