  A qualitative account is given of a differential pursuit/evasion game. A
criterion for the existence of an intercept solution is obtained using future
cones that contain all attainable trajectories of target or interceptor
originating from an initial position. A sufficient and necessary conditon that
an opportunity to intercept always exist is that, after some initial time, the
future cone of the target be contained within the future cone of the
interceptor. The sufficient condition may be regarded as a kind of Nash
equillibrium.

Optimization and Control