An evolutionary game-based vicsek model with a fixed number of neighbors

In the face of collective motion, people often face a binary decision: they may interact with others and pay for communication, or they can choose to go alone and forgo these costs. Evolutionary game theory (EGT) emerges in this setting as a crucial paradigm to address this complex issue. In this study, an EGT-based Vicsek with a fixed number of neighbors is proposed. It assumed that the agent had a limited view and just considered a certain number of neighbors. Agents exhibit varying movement patterns depending on the strategies they choose. Each agent's payoff depends on balancing the benefits of group movement against the communication costs with selected neighbors. Using the Fermi rule, individuals adjust their strategies accordingly. The study indicates that agents achieve the highest levels of cooperation and the fastest convergence times in high-density environments. When density is constant, increasing the number of neighbors enhances the synchronization; when the number of neighbors remains unchanged, a lower density leads to better synchronization. Additionally, the results show that EGT could boost the synchronization and accelerate the convergence of self-propelled agents.