An adaptive neurodynamic approach for solving nonsmooth N-cluster games.

Area of Science:

• Game Theory
• Optimization
• Distributed Systems

Background:

• N-cluster games present complex challenges due to nonsmooth cost functions and interdependencies.
• Finding generalized Nash equilibrium (GNE) in such games is computationally intensive and requires robust methods.

Purpose of the Study:

• To propose a distributed neurodynamic approach for seeking GNE in nonsmooth N-cluster games.
• To address challenges posed by coupling, private constraints, and nonsmooth cost functions.
• To develop a method that avoids prior estimation of penalty parameters.

Main Methods:

• A two-time-scale distributed neurodynamic approach is developed.
• An adaptive leader-following consensus technique is employed for parameter adjustment.
• Primal-dual and adaptive penalty methods are integrated into the framework.

Main Results:

• The proposed approach successfully seeks GNE in nonsmooth N-cluster games.
• The method is completely distributed, requiring no prior knowledge of penalty parameters.
• Player actions are incorporated within constraints during GNE seeking.

Conclusions:

• The neurodynamic approach offers an effective and feasible solution for distributed GNE seeking in complex games.
• The method demonstrates practical applicability through engineering examples in power systems and company capacity allocation.