On a Local Search for Hexamatrix Games

The problem of finding a Nash equilibrium in polymatrix game of three players (hexamatrix game) is considered. For the equivalent nonconvex optimization problem an issue of local search is investigated. First, we study the special local search method (SLSM), based on the linearization of the original problem with respect to basic nonconvexity. Then the new local search procedure is elaborated. This procedure uses the bilinear structure of the objective function and is based on the consecutive solving of auxiliary linear programs. At the end of the paper the results of comparative computational simulation for two local search methods are presented and analyzed.