Defender misled by attackers hiding true speeds in reach games
Deception in Reach-Avoid Game with Unknown Heterogeneous Attackers Speed Information
Computer Science and Game TheoryRobotics
Summary
This work looks at a game where two attackers try to reach a target while one defender tries to stop them. Instead of knowing exactly how fast the attackers can move, the defender only knows a range for each attacker’s speed, but not the exact values. The authors show that attackers can trick the defender by pretending to be slower than they really are, causing the defender to make poor choices. This deception can help attackers get more successes than if everyone’s speeds were fully known.
What this means in practice
- •For security system designers: Design defender strategies that account for uncertain and varied attacker speeds to improve protection in surveillance and border defense.
- •For autonomous vehicle developers: Incorporate uncertainty-aware interception tactics when multiple fast-moving objects approach a protected area with unknown speed capabilities.
Authors
Xiangkai Wu, Shaolin Tan, Wei Wang, Zhen Han
Abstract
This letter investigates a reach-avoid game involving two Attackers and one Defender, where the Attackers aim to maximize the number reaching the target region while the Defender seeks to minimize it. In contrast to conventional complete information formulations, we consider an information asymmetry scenario where the Attackers' heterogeneous maximum speeds are privately known but publicly disclosed to lie within continuous ranges. Existing studies on uncertain speeds, however, have primarily focused on homogeneous settings, whereas heterogeneity extends the uncertainty from a common capability level to the relative capability configuration of the Attackers. To address the resulting capture-order ambiguity over infinitely many possible speed combinations, we establish a critical speed pair framework that characterizes when different capability configurations induce different optimal capture orders, and enables the analysis of the Defender's guessing behavior and the design of information-limiting strategies for the Attackers. We demonstrate that under certain initial conditions, the Attackers can mislead the Defender into making suboptimal decisions through a slow-speed deception strategy, achieving superior payoffs compared to the complete information game. Numerical visualizations reveal the widespread occurrence of such dilemma conditions.