Geodesic
Hybrid global search algorithm with genetic blocks for solving hexamatrix games
The Bulletin of Irkutsk State University. Series Mathematics, Tome 41 (2022), pp. 40-56

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This work addresses the development of a hybrid approach to solving three-person polymatrix games (hexamatrix games). On the one hand, this approach is based on the reduction of the game to a nonconvex optimization problem and the Global Search Theory proposed by A.S. Strekalovsky for solving nonconvex optimization problems with (d.c.) functions representable as a difference of two convex functions. On the other hand, to increase the efficiency of one of the key stages of the global search — constructing an approximation of the level surface of a convex function that generates the basic nonconvexity in the problem under study — operators of genetic algorithms are used. The results of the first computational experiment are presented.
Keywords: polymatrix games of three players, Nash equilibrium, Global Search Theory, local search, level surface approximation, genetic algorithm.
Mots-clés : hexamatrix games 
@article{IIGUM_2022_41_a2,
     author = {Andrei V. Orlov},
     title = {Hybrid global search algorithm with genetic blocks for solving hexamatrix games},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {40--56},
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     url = {http://geodesic.mathdoc.fr/item/IIGUM_2022_41_a2/}
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Andrei V. Orlov. Hybrid global search algorithm with genetic blocks for solving hexamatrix games. The Bulletin of Irkutsk State University. Series Mathematics, Tome 41 (2022), pp. 40-56. http://geodesic.mathdoc.fr/item/IIGUM_2022_41_a2/