Abstract:

The Nash equilibrium game has been applied to many fields, the algorithm for the problem has attracted much attention in recent years. But since the Nash equilibrium game is a complex system composed by a series of optimization problems, the standard optimization method cannot be directly used for the problem, this leads to the difficulty of solving it. For a class of Nash equilibrium games with strongly convex payoff functions, using the Nikaido-Isoda function to transform the Nash equilibrium game into a smooth constraint optimization problem is an effective method to solve the Nash equilibrium game. Based on the gradient strongly monotonity of the Nash equilibrium payoff function, we present a Nikaido-Isoda algorithm for the game and the global convergence of the algorithm is proved. Finally, by solving two kinds of standard Nash equilibrium problems, the feasibility and effectiveness of the Nikaido-Isoda algorithm are verified.

Key words: Nash equilibrium game, Nikaido-Isoda function, constrained optimization problem, strongly convex function