Continuous action iterated dilemma under double-layer network with unknown nonlinear dynamics and its convergence analysis

In this paper, we propose a convergence analysis of evolutionary dynamics with limited learning ability within a double-layer network, exceeding the constraints of current approaches. To model the diversity in the agents' ability to perceive their surroundings, we first design the dynamics model for continuous action iterated dilemma with limited learning ability. The agents are initialized with a fixed parameter that represents their maximum probability of strategy switching during the evolution process. Secondly, we extend the dynamics model to double-layer networks, in which the agents interact exclusively with neighbors in the same layer and update their strategies based on a weighted sum of their payoff in the two layers. Then, we evaluate the environmental influences on learning capacity using a dynamics formula and adapt to the unknown environment dynamics with radial basis function neural network (RBF-NN). Lastly, we conduct a convergence analysis of the dynamics models and confirm their effectiveness with experiments. This method may be utilized to analyze evolutionary processes in hierarchically structured networks.