Prescribed Time Convergence Analysis for Continuous Action Iterated Dilemma with Lyapunov Stability Theory

This paper proposes a new approach for convergence analysis of continuous action iterative dilemma (CAID) to reach a stable consensus outcome within the prescribed time. Unlike usual game theory, where players can only choose between two options, i.e., cooperation or defection, the CAID model lets players pick from varying options and make more nuanced decisions. In the proposed strategy, a prescribed function, which is tunable by the user, adapts the learning rate of the player’s strategy. This new method guarantees that players will eventually agree on a single strategy, regardless of where they started initially, and it achieves this agreement in a predefined time set by the user. The Lyapunov analysis guarantees the convergence of players’ strategies to a consensus within a prescribed time. The simulation results of the proposed scheme with two evolutionary game examples under different communication networks demonstrate faster convergence and fewer iterations compared to the state-of-the-art method.