Generalized `Lion & Man’ Game of R. Rado

In the present work we study the game of degree for generalized "Lion and Man" game where "Lion" L moves on the plane while "Man" M must move along the given curve $\Gamma $ . The case when $\Gamma $ is circumference the problem was formulated by R. Rado and can be considered as the first example of dynamic games. By elementary but refined arguments R. Rado (Littlewood, 1957, Rado, 1973) proved that $L$ can capture $M$ if speeds of both points are equal. Further interesting results on "Lion $\&$ Man" game concerning the case when both points moved inside a circle, was obtained by J. O. Flynn (1973, 1974).