COVID-19 pandemic, a highly infectious disease, has led to unprecedented health and socio-economic crisis worldwide. Accompanied by COVID-19 and its vaccination is an overabundance of misinformation promoting unhealthy practices among individuals. We propose a stratified SIS model incorporating an evolutionary game theoretical framework to help understand the simultaneous progression of pandemic and infodemic when vaccination is available. We consider two domains, disease and information domain, and assume that the information domain consists of the good and bad-behaving individuals. We assume that only the infected individuals with bad information can produce secondary cases of the infection. Findings indicate that the weight of good information does not significantly change the system's dynamics. Instead, it changes the system's stability with low risk requiring a higher weight of good information to arrive at a stable solution of lower infection and higher vaccination. Further, we found that we have an epidemic without misinformation management.