Solving combinatorial problems of gaming type with permutations-restrictions of both players: the interative method

Abstract

The definition and the mathematical model of a game problem for agricultural production with permutations-restrictions that are imposed on the strategies of both players, are considered. The iterative method is extended for combinatorial optimization problems of the gaming type with the restrictions, defined by permutations on the strategies of both players. The method is based on drowing the game, under the condition that each player tries to achieve his goal. A criterion of stopping and the procedures of determination of the result are suggested. On the basis of the developed software computational experiments, which show approaching of payments to the game price, which enables the approximate determination of mixed strategies of the players, are performed. A theoretical and experimental evaluation of the operations of the proposed iterative method is given.