A discrete pursuit-evasion game

Genaro López Acedo

In this talk we focus on a discrete pursuit-evasion game, based on Rado's lion and man problem , defined on a geodesic space. We prove that in uniformly convex bounded domains the lion always wins and, using ideas stemming from proof mining, we extract a uniform rate of convergence for the successive distances between the lion and the man. As a byproduct of our analysis, we study the relation among different convexity properties in the setting of geodesic spaces as well as the relationship between the solution of our game with the seemingly unrelated fixed point property.