Coevolution of individual perception and cooperative behavior in the Norm Compliance Dilemma

Mathematical epidemiology has, now more than ever, attracted great attention in the scientific community. However, little exploration has been done in the direction of modelling human behavioural response when facing an epidemic outbreak. In this context, individuals may employ containment measures to prevent the disease spreading, i.e. providing a benefit to the entire population, at a cost that is heterogeneously perceived by each individual. In our work we study the coevolution of cooperative behaviour and individual perception through the lens of evolutionary game theory, considering the adoption of a disease containment measure as a cooperative act. We introduce this game-theoretical framework as the "Norm Compliance Dilemma", where the evolution of agents’ behaviors depends on their distinct, time-evolving perceptions. Starting from a simplified model of a well-mixed infinite population having homogeneous perceptions, we studied and analytically solved a system of ordinary differential equations to predict the game equilibria. Subsequently, we compared the theoretical results with those obtained in finite populations having heterogeneous individual perceptions and organised in network structures. We show that the disease prevalence promotes cooperation, finding that this result is qualitatively confirmed regardless of the spatial arrangement of individuals or the heterogeneity of their perception. On the other hand, networked structures may hinder and slow down the evolution of cooperation with respect to well-mixed populations. Our model offers an alternative and general methodology to study heterogeneous coevolving perceptions which can be applied to different types of epidemic spreading and norm compliance scenarios.