Deception in Reach-Avoid Game with Unknown Heterogeneous Attackers Speed Information

Xiangkai Wu; Shaolin Tan; Wei Wang; Zhen Han

cs.GTSep 7, 2026

Deception in Reach-Avoid Game with Unknown Heterogeneous Attackers Speed Information

Authors: Xiangkai Wu, Shaolin Tan, Wei Wang, Zhen Han

Organizations: School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China · Zhongguancun Laboratory, Beijing 100094, China · Hangzhou Innovation Institute, Beihang University, Hangzhou 310051, China · China North Vehicle Research Institute, Beijing 100072, China

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.

Figures & tables

Fig. 1: The 2A1D reach-avoid game scenario.

Fig. 2: The illustration of the functions

h_{1},h_{2}

and

h

Panel of Figure 3 — Fig. 3: The visualizations of the dilemma conditions for the given $\mathbf{x}_{A_{1}}$ and $\mathbf{x}_{D}$ with varied position of $\mathbf{x}_{A_{2}}$ . (a) Case 1 with $v_{1}^{\text{max}}=0.3,v_{2}^{\text{max}}=0.3$ , (b) Case 2 with $v_{1}^{\text{max}}=0.61,v_{2}^{\text{max}}=0.65$ .

Game Theory

Game theory studies how interacting decision-makers choose strategies, form agreements, and shape outcomes under competition and cooperation.

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Apr 27, 2026

Asymmetric-Information Resource Allocation Games: An LP Approach to Purposeful Deception

In this work, we introduce the Deceptive Resource Allocation Game (DRAG), which studies purposeful deception within a Bayesian game framework. In DRAG, a Defender allocates resources across the true asset and several decoys to influence an Attacker's beliefs and actions, with the goal of diverting the Attacker away from the true asset. We seek to characterize purposeful deception, whereby the Defender deceives only when doing so improves its performance. To this end, we solve for the Perfect Bayesian Nash Equilibrium (PBNE) of the corresponding game. We show that, despite the coupled belief-policy interdependence, the problem admits an efficient, non-iterative linear programming formulation. Numerical results demonstrate that the resulting policies naturally balance effective allocation and belief manipulation, giving rise to purposeful and emergent deceptive behaviors.

Longxu Pan, Yue Guan, Daigo Shishika +1

Longxu Pan, Yue Guan, and Panagiotis Tsiotras are with the School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA. · Daigo Shishika is with the College of Engineering and Computing, George Mason University, Fairfax, VA, USA.

Imperfect-Information Games Game Theory Linear Programming Nash Equilibrium Computation

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Oct 28, 2026

Minimum-Time Escape from the Conic Field of View of a Reeds--Shepp Pursuer: the Faster Evader

We continue the study of minimum-time escape of an omnidirectional evader from the forward conic field of view of a Reeds--Shepp pursuer, now for a faster evader, and solve the game for every speed ratio

ν>1

and every half-angle

0<α<π/2

: the escape time is characterized by explicit characteristics and the selection of roots of a scalar equation, and it is the value of the game in nonanticipative strategies at every state. Above the end

E

of the evader's dispersal line on the front axis, the evader chases the reversing pursuer along a universal line fed by tributaries. The characteristic from the boundary of the usable part is an involute of a circle of radius

ν

ending at a cusp, and two explicit thresholds decide whether it reaches the axis before the cusp and whether the jump of the escape time across it ends before the cusp or runs to it; in the latter case primaries fold back next to the barrier. The pursuer's optimal strategy is the relay of the slower case. The evader follows the tributaries and switches once to a primary, or commits in advance to a heading certified by the scalar equation of the primaries. Level-set and semi-Lagrangian computations are compared with the value.

Ubaldo Ruiz

Centro de Investigación Científica y de Educación Superior de Ensenada (CICESE), Ensenada, Baja California, Mexico

Game Theory

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Oct 20, 2026

Minimum-Time Escape from the Conic Field of View of a Reeds-Shepp Pursuer: Classification and Game Value for a Slower or Equally Fast Evader

We study minimum-time escape of an omnidirectional evader from the forward conic field of view of a Reeds-Shepp pursuer with minimum turning radius

r

. For speed ratio

ν

and cone half-angle

0<α<π/2

, we prove a global escape/holding classification: straight reversal holds the whole cone for

ν\le\sinα

, escape is confined to a barrier-bounded dart for

\sinα<ν\le1

, and escape is possible from every state for

ν>1

. For the slower or equally fast evader,

\sinα<ν\le1

, we construct the solution with Isaacs' characteristics and verify it in feedback form, using a Filippov pursuer relay and a one-sided evader branch. The finite escape time is the first root of one scalar equation, and the holding region is bounded by the nonusable parts of the rays and a barrier that closes with a convex corner on the front axis. Sample-and-hold counter-controls show that this escape time is the value of the game in nonanticipative strategies at every state except the corner. There the two strategy values differ: the pursuer's is infinite, whereas an evader that chooses which barrier branch to cross from the initial germ of the pursuer's control escapes before the barrier time

τ_I

, which is the evader's exact strategy value. An independent level-set solver, refined on fixed comparison points, agrees with the closed-form escape time and reproduces the holding region at the tested parameters.

Ubaldo Ruiz

Centro de Investigación Científica y de Educación Superior de Ensenada (CICESE), Ensenada, Baja California, Mexico

Game Theory

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Abstract

Game Theory

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