The Role of Space, Density and Migration in Social Dilemmas

Cooperation in multi-agent systems often entails a social dilemma. Cooperators pay a cost to improve public goods whereas defectors free-ride, reaping benefits without incurring any costs or even producing public bads. Much attention has been devoted to understanding cooperation in populations where agents interact with random peers (well-mixed), interact over complex networks, or interact in fixed spatial positions. In spatial settings with mobile agents, however, the effects of cooperation are circumscribed to arbitrary neighbourhoods and the stability of cooperation depends on individuals' capacity to move between sites and form dense clusters. In this paper we study spatial public goods games in which agents either pollute (defectors) or clean (cooperators) their local area and can migrate to empty sites within range. We ask whether migration promotes cooperation and reduces the negative impacts of defection. Analytically and through agent-based simulations, we show that migration ultimately reduces the pollution felt per-capita in at least two ways: 1) polluters encourage eco-friendly neighbours to migrate away, eventually clustering with other cooperators 2) migration stabilises cooperation in dense population scenarios. Our results reveal a complex interaction between migration and density as key factors to promote cooperation in spatial social dilemmas.