Vaccine hesitancy, resulting from bad information, threatens the possibility of ending the COVID-19 pandemic through mass vaccination. The COVID-19 pandemic coincides with an overabundance of controversial information regarding disease transmission and public health mitigation approaches. We investigate a phenomenological co-evolution of pandemic and infodemic in the context of COVID-19 with an emphasis on evolutionary game theory. Using bifurcation analysis, we determine the limit cycle boundaries and the separation of attraction between stable foci of infection and periodic outbreaks of infection. Our results suggest that low risk perception of vaccination relative to infection is not sufficient to eradicate the disease; promotion of quarantine methods or targeted mitigation of the spread of corona-misinformation is necessary to drive the system to disease free equilibrium.