Topological optimization of continuous action iterated dilemma based on finite-time strategy using DQN

In this paper, a finite-time convergent continuous action iterated dilemma (CAID) with topological optimization is proposed to overcome the limitations of traditional methods. Asymptotic stability in traditional CAID does not provide information about the rate of convergence or the dynamics of the system in the finite time. There are no effective methods to analyze its convergence time in previous works. We made some efforts to solve these problems. Firstly, CAID is proposed by enriching the players’ strategies as continuous, which means the player can choose an intermediate state between cooperation and defection. And discount rate is considered to imitate that players cannot learn accurately based on strategic differences. Then, to analyze the convergence time of CAID, a finite-time convergent analysis based on the Lyapunov function is introduced. Furthermore, the optimal communication topology generation method based on the Deep Q-learning (DQN) is proposed to explore a better game structure. At last, the simulation shows the effectiveness of the proposed method.