A global optimization algorithm for solving a four-person game

Abstract

The nonzero sum four-person game was considered. We show that the game can be reduced to a global optimization problem by extending Mills’ result (J Soc Ind Appl Math 8(2):397–402, 1960). For solving the problem, we propose a global optimization method that combines the ideas of the classical multistart and an estimation of a convexity degree of the function. The proposed algorithm was tested numerically on some problems created by the well-known generator GAMUT (GAMUT is a Suite of Game Generators. http://gamut.stanford.edu ) and allowed us to find solutions to the four-person game.