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SCIENCE CHINA Information Sciences, Volume 61, Issue 11: 112206(2018) https://doi.org/10.1007/s11432-017-9408-6

Evasion strategies of a three-player lifeline game

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  • ReceivedSep 13, 2017
  • AcceptedMar 5, 2018
  • PublishedOct 15, 2018

Abstract

This study examines a multi-player pursuit-evasion game, more specifically, a three-player lifeline game in a planar environment, where a single evader is tasked with reaching a lifeline prior to capture. A decomposition method based on an explicit policy is proposed to address the game qualitatively from two main aspects: (1) the evader's position distribution to guarantee winning the game (i.e., the escape zone), which is based on the premise of knowing the pursuers' positions initially, and (2) evasion strategies in the escape zone. First, this study decomposes the three-player lifeline game into two two-player sub-games and obtains an analytic expression of the escape zone by constructing a barrier, which is an integration of the solutions of two sub-games. This study then explicitly partitions the escape zone into several regions and derives an evasion strategy for each region. In particular, this study provides a resultant force method for the evader to balance the active goal of reaching the lifeline and the passive goal of avoiding capture. Finally, some examples from a lifeline game involving more than one pursuer are used to verify the effectiveness and scalability of the evasion strategies.


Acknowledgment

This work was supported by Innovative Research Groups of National Natural Science Foundation of China (Grant No. 61621063) and Key Program of National Natural Science Foundation of China (Grant No. 1613225).


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  • Figure 1

    (Color online) Three-player lifeline game in the plane, where $\varphi$, $\phi_1$, and $\phi_2$ are the moving directions of players E, P$_1$, and P$_2$ in the realistic game space, respectively.

  • Figure 2

    (Color online) Barrier of the two-player lifeline game with $v_p=1.5$, $v_e=1$, and $l=2$.

  • Figure 3

    (Color online) Barrier of the three-player lifeline game with $u=10$, $h_1=5$, $h_2=10$, $l=2$, and $w=1.5$.

  • Figure 4

    (Color online) Force analysis of the evader, where $\alpha$ and $\beta$ are the directions of the forces $F_1$ and $F_2$, respectively, and $\varphi$ is the direction of the resultant force of the evader E.

  • Figure 5

    (Color online) Three-player lifeline game with two different evasion strategies. (a) The evader moves vertically down the lifeline; (b) the evader uses the resultant force strategy (28). The initial positions of the players are E $=(3,15)$, P$_1=(-10,5)$, P$_2=(10,20)$. $w=1.2$ and $l=2$. The black curves are the barriers of the game, the blue, green and red curves are the trajectories of the pursuers P$_1$, P$_2$, and the evader E, respectively.

  • Figure 6

    (Color online) Partition of the escape zone for the three-player lifeline game, where the blue curves are the barriers, and the red curves are described by (25). The initial positions of P$_1$ and P$_2$ are $(-20,5)$ and $(20,20)$, respectively. $w=1.2$ and $l=2$.

  • Figure 7

    (Color online) Lifeline game with more than two pursuers. (a) The evader escapes from three pursuers and reaches the lifeline; (b) the evader escapes from four pursuers and reaches the lifeline. The initial positions of the players are E $=(50,180)$, P$_1=(-200,200)$, P$_2=(200,100)$, P$_3=(300,150)$, and P$_4=(-150,50)$. $w=4/3$ and $l=2$.

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