Theories of pursuit and evasion

Pursuit- Evasion Games

Two players, Red and Blue, each independently choose a vertex of a connected graph G. Red must then pay Blue an amount equal to the distance between the vertices chosen. In this note, w e investigate the value v(G) of this pursuit-evasion game for various classes of graphs G, as well as those optimal mixed strategies for achieving v(G). It is shown that some rather counterintuitive behavior can...

Pursuit/Evasion Voronoi Diagrams∗

In typical 2D Voronoi diagrams, the distance from a site to a point in the plane is unaffected by the existance of other sites. In 2D pursuit/evasion Voronoi diagrams, the distance from an evader to a point is the length of the shortest path to that point that avoids all pursuers. Since pursuers can move, the paths that evaders follow to reach certain points in the plane can be quite complicate...

Pursuit - Evasion Using Beam

A Pursuit-Evasion Toolkit

This tutorial contains tools and techniques for designing pursuit and evasion strategies. The material targets a diverse audience including STEM educators as well as robotics researchers interested in applications of pursuit-evasion games. We start with a simple “lion and man” game in a square environment which should be accessible to anyone with a high-school level background on geometry and t...

Randomized Pursuit-Evasion in Graphs

We analyze a randomized pursuit-evasion game on graphs. This game is played by two players, a hunter and a rabbit. Let G be any connected, undirected graph with n nodes. The game is played in rounds and in each round both the hunter and the rabbit are located at a node of the graph. Between rounds both the hunter and the rabbit can stay at the current node or move to another node. The hunter is...