COMPUTATIONAL STUDY OF HYBRID GLOBAL SEARCH ALGORITHM IN HEXAMATRIX GAMES // BSU Bulletin. Mathematics, Informatics. - 2023. №2. . - С. 14-29.

COMPUTATIONAL STUDY OF HYBRID GLOBAL SEARCH ALGORITHM IN HEXAMATRIX GAMES

Работа выполнена в рамках базового проекта фундаментальных исследо- ваний Минобрнауки РФ «Теоретические основы, методы и высокопроизводи- тельные алгоритмы непрерывной и дискретной оптимизации для поддержки междисциплинарных научных исследований» (Номер гос. регистрации: 121041300065-9, код проекта FWEW-2021-0003).

DOI: 10.18101/2304-5728-2023-2-14-29 UDK: 519.853.6

The paper addresses a special hybrid approach to the de- velopment 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 approx- imation 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.

polymatrix games of three players, hexamatrix games, Nash equilibrium, Global Search Theory, local search, global search algorithm, level surface approximation, genetic operators, hybrid algorithm, compu- tational experiment.