Deception in Differential Games: Information Limiting Strategy to Induce Dilemma

TL;DR

The paper investigates deception by motion in a Turret-Attacker differential game with incomplete information about Attacker speeds, introducing an information-limiting strategy framework. It analyzes both complete-information baselines (1v1 and 2v1) and incomplete-information scenarios, deriving barrier surfaces and reachability sets that partition the state space into Turret-winning and Attacker-winning regions. A central contribution is the Slow-Speed Fast-Heading (SS-FH) information-limiting Attacker strategy, which can force a dilemma for the Turret by concealing true capability, while cases are identified where the Turret can avoid this dilemma. The work provides rigorous definitions, geometric constructions of reachability sets $\mathcal{R}_{1v1}$ and $\mathcal{R}_{2v1}$, and proofs (including $\frac{\partial \tilde{\theta}}{\partial \theta_T} < -1$) that characterize when deception is feasible and how to mitigate it. Overall, the study demonstrates that deception by motion is a viable tactic in asymmetric-information differential games and offers guidelines for designing strategies that either induce or avoid dilemma scenarios.

Abstract

Can deception exist in differential games? We provide a case study for a Turret-Attacker differential game, where two Attackers seek to score points by reaching a target region while a Turret tries to minimize the score by aligning itself with the Attackers before they reach the target. In contrast to the original problem solved with complete information, we assume that the Turret only has partial information about the maximum speed of the Attackers. We investigate whether there is any incentive for the Attackers to move slower than their maximum speed in order to ``deceive'' the Turret into taking suboptimal actions. We first describe the existence of a dilemma that the Turret may face. Then we derive a set of initial conditions from which the Attackers can force the Turret into a situation where it must take a guess.

Figures (11)

• Figure 1: Slow Attackers: one breach ($J=1$) vs zero breach ($J=0$). (a) If the Turret turns CW to capture $A_{2}$ first, then it has sufficient time to capture $A_{1}$ too. (b) If the Turret turns CCW to capture $A_{1}$ first, then $A_{2}$ will be able to breach.
• Figure 2: Fast Attackers: two breaches ($J=2$) vs one breach ($J=1$). (a) Attacker $A_{2}$ cannot be captured even if the Turret turns CW. If the Turret wastes too much time going CW (in hope of capturing $A_{2}$), then $A_{1}$ will also breach. (b) If the Turret turns CCW, at least $A_{1}$ can be captured.
• Figure 3: One vs. one Turret-winning region; in the Turret position shown, it cannot guarantee capture of the Attacker.
• Figure 4: The illustration of the equilibrium strategies for the Runner and Penetrator.
• Figure 5: Venn diagram of trivial cases.

Theorems & Definitions (31)

• Definition 1
• Definition 2: Complete Information Barrier Surface
• Lemma 1
• proof
• Lemma 2
• proof
• Definition 3: 1v1 Intersection and Union
• Definition 4: 2v1 Intersection and Union
• Lemma 3
• proof