Conflict Triangles and Hexamatrix Games

The paper considers one class of finite non-cooperative games (with a finite number of strategies for each player)—E.B. Yanovskaya’s polymatrix games. More specifically, three-player polymatrix games, so-called hexamatrix games (HMGs), which can be completely described by six matrices, are studied. A number of model examples of three-party conflicts, describing some real-life situations, are presented and formulated as HMGs. The feasibility of using hexamatrix games to model economic relationships between three participants is demonstrated. To find the Nash equilibrium in the formulated games, an optimization approach is used, where the equilibrium problem is reduced to a nonconvex optimization problem with a bilinear structure. The latter is solved using A.S. Strekalovskii’s Global Search Theory (GST) for (d.c.) optimization problems with objective functions representable as the difference of two convex functions.