Distributed NE and GNE seeking for heterogeneous multi-player games over directed communication networks

Area of Science:

• Control Theory
• Game Theory
• Distributed Systems

Background:

• Non-cooperative games with heterogeneous dynamics are crucial in fields like autonomous systems and power generation.
• Existing methods for Nash equilibrium (NE) and generalized Nash equilibrium (GNE) seeking often lack applicability to systems with diverse player dynamics and complex network structures.

Purpose of the Study:

• To develop novel distributed strategies for seeking Nash equilibrium (NE) and generalized Nash equilibrium (GNE) in heterogeneous multi-player non-cooperative games.
• To extend existing methodologies to accommodate both undirected and directed communication networks, as well as more complex player dynamics.

Main Methods:

• Utilizing output regulation techniques to design distributed NE seeking strategies for undirected networks.
• Employing Lagrange multipliers and output regulation for distributed GNE seeking under coupled constraints.
• Developing new auxiliary variables to address unbalanced directed communication networks for both NE and GNE seeking.

Main Results:

• A distributed NE seeking strategy was successfully designed for heterogeneous multi-player games over undirected communication networks.
• A distributed GNE seeking strategy was developed, effectively handling coupled constraints among players.
• Novel distributed strategies for NE and GNE seeking were proposed for directed communication networks, extending previous research.

Conclusions:

• The proposed distributed strategies are effective for seeking NE and GNE in heterogeneous multi-player systems, even with complex network topologies.
• The developed methods offer significant improvements over existing approaches by accommodating more general player and network dynamics.
• Numerical simulations validate the effectiveness and robustness of the proposed NE and GNE seeking strategies.