To clean or not to clean: The free-rider problem in sequentially shared resources

Abstract: Shared resources enhance productivity yet at the same time provide channels for biological and digital contamination, turning physical or digital hygiene into a cooperation dilemma prone to free-riding. Here we introduce a game of sequential sharing of common resources, an empirically parameterized evolutionary model of population dynamics in sequential-use settings such as gyms and shared workspaces. The success of the strategies implemented in the model, such as cleaning equipment before or after use, are based on the trade-offs between cleaning costs, contamination risk, and social incentives to mitigate disease transmission. We find that cooperative hygiene can be achieved by lowering the effective costs of cleaning, strengthening pro-social incentives, and monitoring population-level noncompliance. Remarkably, stability of fully altruistic populations is primarily affected by the cleaning costs. In contrast, increasing effective infection costs, for example through punishment, appears less important in this case. The model's evolutionary dynamics exhibit multi-stability, hysteresis, and abrupt shifts in strategy composition, broadly consistent with empirical observations from shared-use facilities. Our framework offers testable predictions and is amenable to quantitative calibration with behavioral and environmental data. Our predictions can be used to inform the design of cost-effective public health and digital security policies.