The monograph developed a variational approach for finding Nash equilibrium situations in a bimatrix game based on reducing this game to some non-convex optimization problem. New algorithms for local and global searches for Nash equilibria have been proposed and substantiated. A multi-stage computational experiment was conducted demonstrating the effectiveness of the developed approach. The results obtained are generalized to the case of bilinear problems with unrelated variables. For specialists in the field of game theory and mathematical programming. On the basis of individual chapters of the monograph, lecture courses for students of mathematical specialties of universities can be given.