A modified Vicsek model based on the evolutionary game

• Published in: Applied mathematics and computation Vol. 438; p. 127565
• Main Authors: You, Feng, Yang, Han-Xin, Li, Yumeng, Du, Wenbo, Wang, Gang
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.02.2023
• Subjects: Collective motion; Communication cost; Evolutionary game theory; Vicsek model; Vicsek model; Communication cost; Collective motion; Evolutionary game theory
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2022.127565

•Considering that individuals can choose to participate or not to participate in collective motion from the perspective of individual interests and group interests.•Further study the influence of communication costs on the choice of individual behavioral strategy.•A modified VM is proposed by introducing the evolution game theory into collective motion, in which different movement modes are designed for the cooperators and the defectors and a reasonable payoff function is proposed.•Numerical simulations have been done to study how the communication radius, the random noise, the relative cost and the density of agents affect the co-evolution of cooperation and synchronization of the proposed model. Despite a large number of studies on collective motion, individuals are usually assumed to participate in flocking unconditionally, and the cost of communication with other individuals is rarely considered. In fact, individuals often need to face a dichotomous scenario: choosing to move together with others and pay the communication cost, or choosing to walk alone and have no communication cost. In this paper, a modified Vicsek model is proposed, in which agents have different kinds of moving patterns depending on the strategies taken by them. Each individual obtains a payoff based on the benefit of the collective motion and the cost of communication with neighbors. Individuals update their strategies according to the evolutionary game theory. It is found that not only cooperation can be maintained, but also the highest synchronization level can be achieved at an optimal value of communication radius. The influence of other pertinent quantities such as the random noise, the relative cost, and the density of agents have also been investigated in detail.