The Convergence Analysis of Evolutionary Dynamics for Continuous Action Iterated Dilemma in Information Loss Networks

In this article, we propose a convergence analysis method for evolution dynamics in information loss networks, which overcomes the analytical difficulties caused by complex network relationships. Evolutionary game theory is a widely-used tool for analyzing player behavior in networks, where players typically adopt binary strategies, either cooperation or defection. However, player behavior in real-world scenarios is often multidimensional and complex, and thus a dynamic model of continuous action iterated dilemma (CAID) with continuous strategy is proposed to enrich the strategies of players, allowing them to choose intermediate states between cooperation and defection, providing a more accurate representation of the evolution of cooperation than traditional dynamic models. Meanwhile, the convergence of traditional models is often analyzed using Jacobian matrices, which requires a significant amount of derivation related to the complex network structure, leading to inefficiencies. As such, a new convergence analysis method based on the Lyapunov function has been designed to circumvent these complex calculations. Additionally, as there is often noise present during the transfer of information between players, we further analyze the convergence of dynamic models in information loss networks using the Lyapunov function. Two examples based on the prisoner's dilemma and snowdrift dilemma on networks are proposed to show the effectiveness of the designed convergence analysis.