This paper shows that prospect theory, extended to account for differences across individuals in their patience and their valuation of the vaccination as a common good can explain why more than 40% of the population has intent to reject the Covid-19 vaccination, as well as the differences in vaccination intentions across population subgroups. Indeed, prospect theory by over-weighting the side effect explains the reject of vaccination. This can be partially compensated by a high patience and/or a large valuation of the collective immunity. The calibrated version of our model, based on an original survey carried out on a representative sample of the adult population living in France allowing us to identify curvatures of their value function, their discount rates and their willingness to cooperate, can predict the evolution of the vaccination intentions between November 2020 an March 2021. We also show that the international differences in the vaccination intentions are closely related to the valuation of the vaccination as a common good.