We analyze, based on an interplay between ideas and techniques from logic and
geometric analysis, a pursuit-evasion game. More precisely, we focus on a uniform
betweenness property and use it in the study of a discrete lion and man game with an
-capture
criterion. In particular, 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.
Keywords
lion and man game, rate of convergence, uniform convexity,
betweenness property