  We consider the asymptotic behavior of solutions to an obstacle problem for
the mean curvature flow equation by using a game-theoretic approximation, to
which we extend that of Kohn and Serfaty (2006). Kohn and Serfaty (2006) give a
deterministic two-person zero-sum game whose value functions approximate the
solution to the level set mean curvature flow equation without obstacle
functions. We prove that moving curves governed by the mean curvature flow
converge in time to the boundary of the convex hull of obstacles under some
assumptions on the initial curves and obstacles. Convexity of the initial set,
as well as smoothness of the initial curves and obstacles, are not needed. In
these proofs, we utilize properties of the game trajectories given by very
elementary game strategies and consider reachability of each player. Also, when
the equation has a driving force term, we present several examples of the
asymptotic behavior, including a problem dealt in Giga, Mitake and Tran (2016).
