Capture of a group of evaders in a conflict-controlled process

The present paper deals with the problem of pursuit of the group of $m$ evaders $(m\geqslant1)$ in a conflict-controlled process with equal opportunities. We say that a multiple capture in the problem of pursuit of one evader ($m=1$) holds if the specified number of pursuers catch him, possibly at different times. The problem of the simultaneous multiple capture of one evader requires that capture moments coincide. We say that the simultaneous multiple capture of the whole group of evaders $(m\geqslant2)$ holds if the simultaneous multiple capture of every evader holds at the same time. We obtain necessary and sufficient conditions for simultaneous multiple capture of the whole group of evaders in terms of initial positions of the participants.