Raid games across a set with cyclic order

In this paper we shall deal with two-person zero-sum games where the strategies of the players are intervals on a set with cyclic order, and the payoff function is a function depending on the intersection of the strategies for the players. These games correspond to similar tactical problems. We give a general method to obtain a solution of the discrete games of this kind. The method is applied to solve the games with monotonic payoff function and a game with no monotonic one. We also solve a continuous game.