Deception in Asymmetric Information Homicidal Chauffeur Game

TL;DR

This paper studies a pursuit-evasion game where the evader can choose from multiple speeds and may use deception to prolong capture, deriving strategies and analyzing when deception is advantageous.

Contribution

It introduces a new asymmetric information variant of the Homicidal Chauffeur game and characterizes when deceptive strategies can increase evasion success.

Findings

Optimal Nash strategies for complete information case.

Regions where deception offers no advantage.

Numerical evidence of deception increasing capture time.

Abstract

The classic Homicidal Chauffeur game is a pursuit-evasion game played in an unbounded planar environment between a pursuer constrained to move with fixed speed on curves with bounded curvature, and a slower evader with fixed speed but with simple kinematics. We introduce a new variant of this game with asymmetric information in which the evader has the ability to choose its speed among a finite set of choices that is unknown to the pursuer a priori. Therefore the pursuer is required to estimate the evader's maximum speed based on the observations so far. This formulation leads to the question of whether the evader can exploit this asymmetry by moving deceptively by first picking a slower speed to move with and then switching to a faster speed when a specified relative configuration is attained to increase the capture time as compared to moving with the maximum speed at all times. Our contributions are as follows. First, we derive optimal feedback Nash equilibrium strategies for the complete information case of this game in which the evader is allowed to vary its speed in a given interval. Second, for the version with asymmetric information, we characterize regions of initial player locations in the game space from which the evader does not have any advantage in using deceptive strategies. Finally, we provide numerical evidence of regions in the game space from which the evader can increase the capture time by moving deceptively.