Vaccination game theory typically assumes homogeneous populations. In this paper, we develop and solve a vaccination game for an infinite population of agents with non-homogeneous preferences. We assume that agents may vary in how susceptible they are to the disease and how they perceive the cost of the disease and cost of the vaccination, and they may also vary in how they perceive vaccine effectiveness. We encode this heterogeneity by a quantile function describing the distribution of the net relative vaccination cost and give an explicit formula for the Nash equilibrium of the game. We show how this theory can be applied to real-world data and we compare our method to its homogeneous counterpart. We observe that overall, our method outperforms the homogeneous method; the difference in the performance is especially striking when only a small number of survey results are available. Overall, our method is also more robust and provides smaller prediction errors.