An Improved Lion Strategy for the Lion and Man Problem

"Lion and Man": Upper and Lower Bounds

Revised: The Lion and Man Game on Convex Terrains

We study the well-known lion-and-man game in which a lion (the pursuer) tries to capture a man (the evader). The players have equal speed and they can observe each other at all times. In this paper, we study the game on the surface of convex terrains. We show that the lion can capture the man in finite number of steps which is a function of the terrain geometry.

The Lion and Man Game on Convex Terrains

We study the well-known lion-and-man game in which a lion (the pursuer) tries to capture a man (the evader). The players have equal speeds and they can observe each other at all times. While the game is well-studied in two dimensional domains such as polygons, very little is known about its properties in higher dimensions. In this paper, we study the lion and man game on the surface of convex t...

Shy Couplings, Cat(0) Spaces, and the Lion and Man

Two random processes X and Y on a metric space are said to be ε-shy coupled if there is positive probability of them staying at least a positive distance ε apart from each other forever. Interest in the literature centres on nonexistence results subject to topological and geometric conditions; motivation arises from the desire to gain a better understanding of probabilistic coupling. Previous n...

Lion and Man with Visibility in Monotone Polygons

In the original version of the lion and man game, a lion tries to capture a man who is trying to escape in a circular arena. The players have equal speeds. They can observe each other at all times. We study a new variant of the game in which the lion has only line-of-sight visibility. That is it can observe the man’s position only if the line segment connecting them does not intersect the bound...