Triangles of conflicts and hexamatrix games

Abstract

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.