A Convergence Study on the Continuous Action Iterated Hierarchical Dilemma Model with Asymmetric Learning Mechanism

Analyzing the convergence of social networks is still challenging for the existing investigations, which are always in disregard of the individuals' own social hierarchy and interindividual hybrid learning patterns during the interactive relationship modelings. To fill this gap, we propose a Continuous Action Iterated Hierarchical Dilemma (CAIHD) model to adequately characterize the real-world social networks by means of capturing all individuals' situated hierarchical relationships and adjustable interaction weights, called asymmetric learning mechanism. Further, we absorb the general Lyapunov potential function into our given theorem to theoretically prove that the asymptotic convergence often exists in the social networks when the property of strongly connected and balance graph holds. Finally, we perform numerical experiments on multiscale social networks and the empirical results shed lights on the great potentials of our CAIHD model in promoting convergence study on the larger-scale social network.