Geodesic
Triangles of conflicts and hexamatrix games
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 16 (2024) no. 4, pp. 69-94

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The paper addresses one class of finite non-cooperative games (with finite numbers of strategies for each player) – Polymatrix Games of E.B. Yanovskaya. Namely, we study in detail the 3-players Polymatrix Games, the so-called Hexamatrix Games (HMG), which can be completely described by six matrices. A number of model examples of 3-sides real-life conflicts are presented and formulated as HMG. The possibility of using hexamatrix games to model economic relationships between three participants is demonstrated. To find a Nash Equilibrium in the formulated games, we use an optimization approach, when the problem is transformed into a nonconvex optimization problem with a bilinear structure. The latter is solved by the A.S. Strekalovsky’s Global Search Theory (GST) for (d.c.) optimization problems with objective functions represented as the difference of two convex functions.
Keywords: finite noncooperative games, Nash equilibrium, nonconvex optimization problems, local and global search algorithms, computational experiment.
Mots-clés : polymatrix games, hexamatrix game 
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     author = {Andrey V. Orlov},
     title = {Triangles of conflicts and hexamatrix games},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {69--94},
     publisher = {mathdoc},
     volume = {16},
     number = {4},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2024_16_4_a3/}
}
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Andrey V. Orlov. Triangles of conflicts and hexamatrix games. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 16 (2024) no. 4, pp. 69-94. http://geodesic.mathdoc.fr/item/MGTA_2024_16_4_a3/