We consider a vaccination game that results with the introduction of premature and possibly scarce vaccines introduced in a desperate bid to combat the otherwise ravaging deadly pandemic. The response of unsure agents amid many uncertainties makes this game completely different from the previous studies. We construct a framework that combines SIS epidemic model with a variety of dynamic behavioral vaccination responses and demographic aspects. The response of each agent is influenced by the vaccination hesitancy and urgency, which arise due to their personal belief about efficacy and side-effects of the vaccine, disease characteristics, and relevant reported information (e.g., side-effects, disease statistics etc.). Based on such aspects, we identify the responses that are stable against static mutations. By analysing the attractors of the resulting ODEs, we observe interesting patterns in the limiting state of the system under evolutionary stable (ES) strategies, as a function of various defining parameters. There are responses for which the disease is eradicated completely (at limiting state), but none are stable against mutations. Also, vaccination abundance results in higher infected fractions at ES limiting state, irrespective of the disease death rate.