  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.
