Abstract The vaccination game exhibits positive externalities. The standard game-theoretic approach assumes that parents make decisions according to the Nash protocol, which is individualistic and non-cooperative. However, in more solidaristic societies, parents may behave cooperatively, optimizing according to the Kantian protocol, in which the equilibrium is efficient. We develop a random utility model of vaccination behavior and prove that the equilibrium coverage rate is larger with the Kant protocol than with the Nash one. Using survey data collected from six countries, we calibrate the parameters of the vaccination game, compute both Nash equilibrium and Kantian equilibrium profiles, and compare them with observed vaccination behavior. We find evidence that parents demonstrate cooperative behavior in all six countries. The study highlights the importance of cooperation in shaping vaccination behavior and underscores the need to consider these factors in public health interventions.