<p>Vaccination plays a pivotal role in controlling epidemic transmission. However, individuals must weigh the benefits of vaccination against the perceived risks of infection when making personal health decisions. Understanding the complex interplay between these individual choices and their collective impact on population-level epidemic dynamics is essential for effective disease management. In this study, we develop a game-theoretic SIR model to investigate the dynamic relationship between individual vaccination behavior and epidemic spread in an age-heterogeneous population. We derive the basic reproduction number and analyze the stability of each feasible equilibria. Then, we strictly prove the existence of Hopf bifurcation derived by both introduction of the age heterogeneity and the evolutionary vaccination strategy. Our results uncover the emergence of free-riding behavior and oscillating Nash equilibria. Moreover, numerical simulations reveal that age-dependent infectiousness can intensify epidemic oscillations, while the incorporation of vaccination strategies may further enhance these cyclical patterns.</p>