On the interrelationship of two problems on evasion with many evaders

The problem of evasion is considered in which a group of pursuers and a group of evaders participate under the condition that the pursuers include both participants whose capabilities do not yield place to the capabilities of the evaders and participants with lesser capabilities. The aim of the group of pursuers is to capture all the evaders. The aim of the group of evaders is to prevent the capture, i.e., to make it possible for at least one of the evaders to avoid an encounter. The pursuers and the evaders employ piecewise-program strategies. It is shown that, if in a differential game at least one evader avoids the encounter on an infinite time interval, then upon the addition of “weak” pursuers evasion will take place on any finite time interval.