Fixed time convergence approach for multiplayer iterated dilemmas with continuous action

This paper introduces a novel fixed-time scheme for analyzing the convergence of the multiplayer continuous action-iterated dilemma (CAID). In contrast to conventional evolutionary game theory, which restricts players to binary strategies of cooperation or defection, CAID allows for continuous strategies and offers players a spectrum of choices. Additionally, two discount rates are incorporated in the strategy dynamics to reflect the imprecision in players' learning from strategic differences. The proposed algorithm ensures a fixed-time convergence of consensus between the player strategies. As a result, the settling time of consensus is independent of the initial strategy. Lyapunov stability theory is employed to assess convergence within a fixed time. Moreover, simulation results demonstrate the superiority of the proposed algorithm, converging more quickly and with fewer iterations than the recently established results.