Searching Positive-Incentive Noise from Optimal Consensus in Continuous Action Iterated Dilemma

In this paper, an analysis-definition-processing (ADP) framework is proposed to search positive-incentive noise in continuous action iterated dilemma (CAID). We analyze the influence of communication noise on the cooperative behavior of players in the system and introduce the concept of positive-incentive noise in CAID. We design a global cost function to ensure convergence of the system can be achieved and strive to improve the final level of cooperation. An optimal CAID control method is proposed to derive the deterministic optimal learning rate in analytical form, avoiding the variability and uncertainty brought about by neural network fitting or parameter adjustment. On this basis, the convergence of the dynamic model is further analyzed by using the Lyapunov function instead of the Jacobian matrix. Additionally, an adaptive filtering mechanism is designed to dynamically ensure that only positive-incentive noise affects the system, effectively reducing the impact of negative noise and enhancing system stability. The framework is validated through simulations involving triple classical game models, including the hawk-dove game, the stag hunt game, the chicken game on networks, and a straightforward illustrative example.