This paper constructs a family of discrete games, whose value functions converge to the unique viscosity solution of the Neumann boundary problem of the curve shortening flow equation. To derive the boundary condition, a billiard semiflow is introduced and its basic properties near the boundary are studied for convex and more general domains. It turns out that Neumann boundary problems of mean curvature flow equations can be intimately connected with purely deterministic game theory.
"A billiard-based game interpretation of the Neumann problem for the curve shortening equation." Adv. Differential Equations 14 (3/4) 201 - 240, MArch/April 2009. https://doi.org/10.57262/ade/1355867265