Exact Time Continuous Action Iterated Dilemma Under Time Delay and Information Lossy Network

The classical game theory provides a useful tool to analyze the agent’s (or player’s) behavior, often limited to binary choices, i.e., cooperation or defection. However, real-world agent behavior is typically nuanced. This article leverages a continuous action iterated dilemma (CAID) framework, allowing players to adopt a varied range of strategies between two binary decisions. Moreover, most studies presume all agents to have perfect communication networks, neglecting the complexities of real-world networks, such as delays, model uncertainties, and information losses. In this regard, this work presents a new exact-time (ExT) convergent CAID strategy, considering the communication delays during data transmission and information loss in complex networks. The conventional convergence analysis typically relies on Jacobian matrices, which consider a strong correlation between players and, therefore, struggle when dealing with complex player relationships. In contrast, the proposed ExT algorithm ensures consensus among all players, irrespective of the initial conditions, within a preset time selected by the user. The CAID model’s convergence is analyzed using Lyapunov theory and Artstein’s transformation, which validates the ExT convergence to the consensus value amidst communication delays and information loss. Extensive simulations reveal that the proposed strategy consistently outperforms existing methods in terms of convergence speed.