Complex Continuous Action Iterated Dilemma with Incremental Dynamic Model

In this article, we propose a complex continuous action iterated dilemma (CAID) with an incremental dynamic approach to overcome the limitations of traditional methods. In traditional CAID, the number of players was fixed. Consequently, when new players joined, computing resources were wasted due to repeated refreshes during the dynamic update process. To address these issues, we first propose a CAID model with an incremental dynamic approach. This model reflects the dynamic changes in the number of players, aligning more closely with real-world scenarios. Second, we propose an incremental updating method to prevent unnecessary refreshes of the original players' states. When the number of players, denoted as N , increases, we update and expand the evolutionary dynamic model using incremental information. This allows for an incremental connection between the original and new players. We use a weighted adjacency matrix to represent the relationships among players. The incremental updating method then updates the state matrix and the adjacency matrix. Furthermore, an analysis based on the designed Lyapunov function is proposed to prove the convergence of the CAID with incremental dynamic. The simulation results reveal the effectiveness of our proposed method.