The book examines the tasks of optimizing the procession in a conflict situation when the process is controlled by two opposing parties. Studies are continuous, described by ordinary differential equations, and discrete, described by differential equations, processes. The optimality of the process is understood in the sense of minimax or maximin functionality from the phase coordinates of the process according to the control parameters of the opposing parties in the case of strict rivalry and in the sense of the maximum functionality for each of the controlling parties in case of weak rivalry.