  We study a variant of pursuit-evasion game in the context of perimeter
defense. In this problem, the intruder aims to reach the base plane of a
hemisphere without being captured by the defender, while the defender tries to
capture the intruder. The perimeter-defense game was previously studied under
the assumption that the defender moves on a circle. We extend the problem to
the case where the defender moves on a hemisphere. To solve this problem, we
analyze the strategies based on the breaching point at which the intruder tries
to reach the target and predict the goal position, defined as optimal breaching
point, that is achieved by the optimal strategies on both players. We provide
the barrier that divides the state space into defender-winning and
intruder-winning regions and prove that the optimal strategies for both players
are to move towards the optimal breaching point. Simulation results are
presented to demonstrate that the optimality of the game is given as a Nash
equilibrium.
