Rubella is a highly contagious childhood disease that causes relatively mild symptoms. However, rubella can result in severe congenital defects, known as congenital rubella syndrome (CRS), if transmitted from a mother to a fetus. Consequently, women have higher incentive to vaccinate against rubella than men do. Within the population vaccination reduces transmission but also increases the average age of infection and possibly the risk of CRS among unvaccinated females. To evaluate how the balance among these factors results in optimal coverage of vaccination, we developed a game theoretic age-structured epidemiological model of rubella transmission and vaccination. We found that high levels of vaccination for both genders are most effective in maximizing average utility across the population by decreasing the risk of CRS and reducing transmission of rubella. By contrast, the demands for vaccines driven by self-interest among males and females are 0% and 100% acceptance, respectively, if the cost of vaccination is relatively low. Our results suggest that the rubella vaccination by males that is likely to be achieved on voluntary basis without additional incentives would have been far lower than the population optimum, if rubella vaccine were offered separately instead of combined with measles and mumps vaccination as the MMR vaccine.