  This paper studies a variant of multi-player reach-avoid game played between
intruders and defenders. The intruder team tries to score by sending as many
intruders as possible to the target area, while the defender team tries to
minimize this score by intercepting them. Specifically, we consider the case
where the defenders are constrained to move on the perimeter of the target
area. Since it is challenging to directly solve the multi-player game due to
the high dimensionality of the joint state space, we leverage the solutions to
smaller scale problems. First, we solve the one vs. one game, for which
existing works either rely on numerical approaches or make simplifying
assumptions (e.g., circular perimeter, or equal speed). This paper accommodates
target areas with any arbitrary convex shapes and provides analytical solution
which lends itself to a useful geometric interpretation. We also provide a
detailed discussion on the optimality of the derived strategies. Secondly, we
solve the two vs. one game to introduce a cooperative pincer maneuver, where a
pair of defenders team up to capture an intruder that cannot be captured by
either one of the defender individually. Finally, we introduce how the
aforementioned building blocks are used in three different assignment-based
defense strategies.
