STP-based control of networked evolutionary games with multi-channel structure

Area of Science:

• Game Theory
• Network Science
• Control Theory

Background:

• Channel delay significantly impacts evolutionary game dynamics.
• Previous work focused on state delays; control delays are newly introduced.
• Strategy propagation time is a critical factor in real-world games.

Purpose of the Study:

• To optimize strategy games with both state and control delays.
• To develop a framework for analyzing evolutionary game dynamics under general information delays.
• To design feedback controllers for strategy optimization in networked environments.

Main Methods:

• Utilizing the semi-tensor product of matrices to transform game dynamics into an algebraic form.
• Analyzing six distinct cases based on control and state delay values.
• Employing a reachable set method for feedback controller design.

Main Results:

• Derived sufficient and necessary conditions for strategy optimization existence.
• Successfully designed feedback controllers based on algebraic equations.
• Demonstrated the model's feasibility through an illustrative example.

Conclusions:

• The proposed semi-tensor product method effectively models networked evolutionary games with delays.
• The findings provide a robust framework for addressing game-based control in complex networks.
• This research offers valuable insights for understanding and managing evolutionary dynamics in delayed systems.