Multi-player pursuit–evasion games with one superior evader

Abstract

Inspired by the hunting and foraging behaviors of group predators, this paper addresses a class of multi-player pursuit-evasion games with one superior evader, who moves faster than the pursuers. We are concerned with the conditions under which the pursuers can capture the evader, involving the minimum number and initial spatial distribution required as well as the cooperative strategies of the pursuers. We present some necessary or sufficient conditions to regularize the encirclement formed by the pursuers to the evader. Then we provide a cooperative scheme for the pursuers to maintain and shrink the encirclement until the evader is captured. Finally, we give some examples to illustrate the theoretical results.

Revisiting a Three-Player Pursuit-Evasion Game

“…On the other hand, the BUP is on both nonusable surfaces (corresponding to capture); hence, the trajectory may start (in reverse time) along such a surface. After an arbitrary 4 time, the trajectory diverges from the surface and, being in the interior, obeys the equations derived previously. We state without proof that both d i distances strictly increase (still in retrograde time) after such a junction point; therefore, the trajectory will never meet a nonusable surface again.…”

“…For this, we will reverse the connection: calculate the path parameters from the initial state. In the future, we aim to use these results in solving a game where the superior evader has been encircled by three (or more) pursuers and has to escape [4,13].…”

Survey on spacecraft orbital pursuit-evasion differential games

“…Hayoun和Shima [49] 对 一阶动力学模型下具有控制边界的二追一问题进行了 分析性研究. Chen等人 [50] 模拟"捕猎"问题研究了多追 踪器追踪一个高速逃逸器的最优策略. Scott和Leonard [51] 分析了单个追踪器和多个逃逸器进行博弈时的 最优逃逸策略, 在运动参数上给出了很多限制.…”

Generalized Cops and Robbers: A Multi-player Pursuit Game on Graphs

“…So in this example P 2 and P 3 's optimal Γ 2 (G|s 0 ) strategies are not good (and certainly not in NE) in Γ 3 (G|s 0 ). 5 We define ρ 1 such that, when combined with s T 1 −1 , φ 2 1 , φ 3 1 , will produce the same history s T 1 s T 1 +1 s T 1 +2 ... as σ 1 . Note that ρ 1 will in general depend (in an indirect way) on s 0 s 1 ... s T 1 −2 .…”

“…It is also remarkable that, while classic CR and many of its variants admit a natural game theoretic formulation and study, this has not been exploited in the CR literature.Regarding pursuit in Euclidean spaces, the predominant approach is in terms of differential games as introduced in the seminal book [10]. There is a flourishing literature on the subject, which contains many works involving multiple pursuers, but they are generally assumed to be collaborating [5,11,15,18,19]. The case of antagonistic pursuers has been studied in some papers [8,9] but the methods used in these works do not appear to be easily applicable to the study of pursuit / evasion on graphs.This paper is organized as follows.…”