In this research, we investigate the evolution of cooperation in a complex system, namely the healthcare system in England, which is made up of populations consisting of different healthcare providers interacting with patients. Our investigation examines individual agents’ behaviors as viewed by an external policymaker, in this case, the Health Department. Generally, policies are initiated and managed by the Health Department, which allocates a specific budget to interfere. To this end, our analysis here is carried out based on a baseline model we developed in [1]. This previous work focuses on numerical analysis of the proposed healthcare model, studying evolutionary dynamics of three well-mixed finite populations. The analytical approach we adopted therein relied on the assumptions of rare behavioral mutation by the agents, and that all populations having an equal size. Our finding shows that agents from all three populations tend to not cooperate (i.e. defect) [1]. While these simplified assumptions allowed us, as a very first step, to provide clear mathematical analysis, they prevented us from analyzing some important factors. Namely, mutation or behavioral exploration, where agents can freely experiment with new behaviors, has been shown to play an important role in enabling cooperation in the context of social dilemmas [2]. Overall our finding shows cooperation tends to increase with NS when bR is sufficiently large, while it tends to decrease with NS when bR is small. That is, trying to meet patients’ demand only has a positive effect on cooperation outcomes if providers’ benefit is secured, regardless of high patients’ benefit (i.e bR =3).
