Games and flocks: Switching strategies applied to the Couzin model

This study investigates the integration of game theory into agent-based models of collective motion. We build upon the integration of game theory with the Vicsek Model, extending it to a more biologically realistic setting by incorporating the Couzin Model. Specifically, we incorporate strategies of cooperation and defection, where cooperators follow the Couzin Model updating laws, and defectors update directions randomly. The agents update their strategies based on local order, which serves as an indicator of the benefits of their current strategy at each time-step. The results indicate that by modifying the payoff for grouping, a phase transition is observed, transitioning from a swarm-like state to a state of heightened synchronization. Additionally, altering the level of rationality of agents affects the length of the transition region between the two critical points. The level of rationality refers to how decisively agents respond to differences in local order. As agents become more irrational, they may change strategies even when the difference in local order is small. In the unstable transition region, we observed that the same parameter could yield opposite results. Moreover, we identified a unique behavior where a defector approached a cooperative group, leading to its disintegration in a manner reminiscent of a predator attacking a group of fish in nature. This phenomenon has been observed exclusively in the Couzin model and is not present in previous game theory with the Vicsek Model.