Optimal growth trajectories with finite carrying capacity

We investigate the spatial Public Goods Game in the presence of conformity-driven agents on a bi-dimensional lattice with periodic boundary conditions. The present setting usually considers fitness-driven agents, i.e., agents that tend to imitate the strategy of their fittest neighbors. Here, fitness is a general property usually adopted to quantify the extent to which individuals are able to succeed, or at least to survive, in a competitive environment. However, when social systems are considered, the evolution of a population might be affected also by social behaviors as conformity, stubbornness, altruism, and selfishness. Although the term evolution can assume different meanings depending on the considered domain, here it corresponds to the set of processes that lead a system towards an equilibrium or a steady-state. In doing so, we use two types of strategy update rules: fitness-driven and conformity-driven. We map fitness to the agents’ payoff so that richer agents are those most imitated by fitness-driven agents, while conformity-driven agents tend to imitate the strategy assumed by the majority of their neighbors. Numerical simulations aim to identify critical phenomena, on varying the amount of the relative density of conformity-driven agents in the population, and to study the nature of related equilibria. Remarkably, we find that conformity fosters ordered phases and may also lead to bistable behaviors.