Optimal Evolution Strategy for Continuous Strategy Games on Complex Networks via Reinforcement Learning.

Area of Science:

• Game Theory
• Artificial Intelligence
• Network Science

Background:

• Traditional evolutionary game theory assumes uniform agent learning intensity, neglecting individual differences.
• Agents often exhibit reluctance to significantly alter strategies, limiting cooperation levels.

Purpose of the Study:

• To develop an adaptive strategy updating framework for continuous games on complex networks.
• To enable agents to achieve optimal states and higher cooperation with minimal strategy modifications.

Main Methods:

• An adaptive framework based on imitation dynamics with varied selection intensities.
• Coupled Hamilton-Jacobi-Bellman (HJB) equations to derive optimal strategy updates by minimizing a performance function.
• A value iteration (VI) reinforcement learning (RL) algorithm with actor-critic neural networks to approximate HJB solutions.

Main Results:

• The proposed RL algorithm effectively learns optimal strategy updating rules.
• Stability and convergence of the methods were mathematically proven using Lyapunov functions.
• Simulations confirmed the effectiveness and convergence across diverse games and network structures.

Conclusions:

• The adaptive strategy framework enhances cooperation in complex network games.
• Reinforcement learning provides an effective approach to solving continuous strategy games.
• Minimal strategy changes lead to optimal outcomes and higher cooperation levels.