Open-minded imitation can achieve near-optimal vaccination coverage

Game-theoretic studies of voluntary vaccination predict that a socially unstructured population that is guided exclusively by individual rational self-interest always reaches a Nash equilibrium with vaccination coverage that is below the societal optimum. Human decision-making involves additional mechanisms, such as imitation of the successful strategies of others. However, previous research has found that imitation leads to vaccination coverage that is even below the Nash equilibrium. In this work, we note that these conclusions rely on the widely accepted use of Fermi functions for modeling the probabilities of switching to another strategy. We consider here a more general functional form of the switching probabilities. It involves one additional parameter a. This parameter can be loosely interpreted as a degree of open-mindedness. The resulting dynamics are consistent with the ones that would be generated by functions that give best fits for empirical data in a widely cited psychological experiment. We show that sufficiently high levels of open-mindedness, as conceptualized by our parameter a, will drive equilibrium vaccination coverage levels above the Nash equilibrium, and in fact arbitrarily close to the societal optimum. These results were obtained both through mathematical analysis and numerical simulations.