A Computational Method for Solving $N$-Person Game

Abstract

The nonzero sum $n$-person game has been considered. It is well known that the game can be reduced to a global optimization problem [5; 7; 14]. By extending Mills’ result [5], we derive global optimality conditions for a Nash equilibrium. In order to solve the problem numerically, we apply the Curvilinear Multistart Algorithm [2; 3] developed for finding global solutions in nonconvex optimization problems. The proposed algorithm was tested on three and four person games. Also, for the test purpose, we have considered competitions of 3 companies at the bread market of Ulaanbaatar as the three person game and solved numerically.

Keywords

• Nash equilibrium
• nonzero sum game
• mixed strategies
• curvilinear multistart algorithm