Distributed Nash Equilibrium Seeking Over Markovian Switching Communication Networks

Area of Science:

• Game Theory
• Networked Systems
• Distributed Algorithms

Background:

• Finding Nash equilibrium (NE) is crucial for strategic decision-making in multi-player systems.
• Existing methods often struggle with dynamic network conditions and distributed control.

Purpose of the Study:

• To develop a novel distributed synchronous discrete-time algorithm for Nash equilibrium seeking.
• To analyze the convergence and stability properties of the proposed algorithm in Markovian switching networks.

Main Methods:

• A gradient-like projection algorithm is employed by each player.
• Convergence is analyzed under the condition of a connected union network.
• Mean-square stability of the Nash equilibrium is investigated.

Main Results:

• The proposed algorithm ensures players' actions converge to a small neighborhood of the Nash equilibrium in the mean-square sense.
• The unique Nash equilibrium is shown to be mean-square stable without constraints.
• The algorithm's applicability to microgrid energy trading is demonstrated.

Conclusions:

• The developed distributed algorithm effectively addresses Nash equilibrium seeking in complex networked environments.
• This approach offers a viable solution for decentralized problems like microgrid energy trading.
• Numerical simulations validate the algorithm's performance and practical utility.