Ryzhkova I. Problems of pursuit-evation in linear games with constrains on resources

Thesis is devoted to games with integrated restrictions on the players controls with simple moving, with a simple matrix and with an arbitrary matrix. The sets of initial positions favorable to this or that player and the optimum strategies of the players are constructed. The methods which reduce games with integrated restrictions to games with geometrical restrictions are developed. These methods are generalization of a method of Н-convex sets. At a solution of games with an arbitrary matrix the property "of a complete sweeping " which was transferred from sets on function is used, that has allowed to reduce game to a control problem. With the help of matrix convexity and Н-convexity the problem of deduction for game with an arbitrary matrix is solved.