Computational study of hybrid global search algorithm in hexamatrix games

The paper addresses a special hybrid approach to the development of methods for finding Nash equilibrium points in three-person polymatrix games (hexamatrix games). On the one hand, this approach is based on the Global Search Theory created by A.S. Strekalovsky for nonconvex optimization problems with d.c. functions (representable as a difference of two convex functions). On the other hand, to implementation of one of the key stages of the global search - constructing an approximation of the level surface of a convex function - operators of genetic algorithms are used. After the description of the hybrid approach, it is described in detail about the organization and carrying out of an extensive computational experiment comparing the hybrid algorithm with the ”basic” global search algorithm developed earlier. The results of a computational experiment on a series of randomly generated problems are presented, which confirm the efficiency of the proposed hybrid approach to solving hexamatrix games.