Defender misled by attackers with hidden different speeds in pursuit game
Deception in Reach-Avoid Game with Unknown Heterogeneous Attackers Speed Information
Computer Science and Game TheoryRobotics
Summary
This paper looks at a game where two attackers try to reach a target while one defender tries to stop them. The challenge is that the attackers know their own top speeds but only reveal that their speeds fall somewhere within certain ranges, and these speeds vary between the attackers. The authors show that this uncertainty can confuse the defender about which attacker is faster, leading to mistakes. They find that attackers can use this confusion by pretending to be slower to trick the defender and improve their chances of success. The study explains when and how this deception works and shows that it happens often under certain starting conditions.
reach-avoid gameinformation asymmetryheterogeneous speedscapture-ordergame theoryoptimal strategyspeed uncertaintydefender-attacker modeldeception strategy
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.