  A new family of pursuit strategies is introduced for a multi-pursuer
single-evader game. By exploiting the optimal solution of the game involving
two pursuers, conditions are derived under which the multi-pursuer game becomes
equivalent to the two-pursuer one. This opens the possibility of designing a
number of pursuit strategies in which the pursuers first try to enforce the
satisfaction of the aforementioned condition and then switch to a two-pursuer
game as soon as it is verified. The contribution is useful in two ways. First,
new winning pursuit strategies can be devised starting from simple plans, such
as pure pursuit. Moreover, the performance of existing pursuit strategies, like
those based on Voronoi partitions, can be significantly improved by resorting
to the corresponding switching version.
