Practical fixed-time consensus for continuous action iterated dilemmas under communication and learning constraints

This paper introduces a continuous action iterated dilemma (CAID) model, enabling agents to adopt a spectrum of strategies beyond the traditional game theory practice of having only binary options. Existing research on the CAID problem often overlooks real-world challenges and assumes perfect communication and learning rates among agents. This work considers the limitations of complex networks, such as communication delays, restricted learning rates of agents, dynamic uncertainty, and information losses during data transmission. The proposed strategy employs a fixed-time convergent algorithm with Artstein transformation that transforms a delay-induced system into a delay-free model, and the fixed-time design ensures consensus among all agents within a fixed and bounded timeframe, regardless of the initial conditions. The convergence analysis of the proposed CAID strategy is conducted using Lyapunov theory, validating the practical fixed-time convergence of consensus despite communication delays, confined learning rates, model uncertainty, and information loss. Numerical simulations under varying conditions demonstrate that the proposed approach facilitates faster consensus attainment and requires fewer iterations than the existing method.