Analysis of the n-person noncooperative supermodular multiobjective games

This paper investigates a class of noncooperative multiobjective games in the supermodular form played by a finite number of players. We prove the existence of two different equilibria of those games, namely, the Pareto equilibrium and the weighted Nash equilibrium. Using Python programming, we apply a genetic algorithm to obtain the Pareto equilibrium and a modified payoff matrix to obtain the weighted Nash equilibrium. We demonstrate the application of our result in an inventory game problem.