A Finite-Time Convergent Analysis of Continuous Action Iterated Dilemma

In this letter, a finite-time convergent analysis of continuous action iterated dilemma (CAID) is proposed. In traditional evolutionary game theory, the strategy of the player is binary (cooperation or defection), which limits the number of strategies a player can choose from. Meanwhile, there are no effective methods to analyze the convergence and its convergence time in previous works. To solve these problems, we make several innovations in this letter. 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 of CAID, the Lyapunov function is designed. Furthermore, to analyze the convergence time of CAID, a finite-time convergent analysis based on the Lyapunov function is introduced. In this case, simulation results show the effectiveness of our analysis.