Vasil'ev

A general case of weakly investigated N-person matrix games was considered in this paper. The brute force Nash equilibrium method for mixed strategies, known in case of N = 2, was successfully generalized. Computational complexity of this algorithm is unacceptable; this algorithm is reduced to solving exponentially increasing (depending on the number of strategies) number of completed linear systems, where the number of variables also exponentially depends on N. The new playing equilibrium algorithm based on the methods of linear programming and duality theory was proposed in this work. The algorithm was developed with the use of a more simple auxiliary coalition-free game introduced by means of some problem of mathematical programming. An example of the numerical solution of a 3-person game is given in the article.