Strain competition plays an important role in shaping the dynamics of multiple pathogen outbreaks in a population. Competition may lead to exclusion of some pathogens, while it may influence the invasion of an emerging mutant in the population. However, little emphasis has been given to understand the influence of human vaccination choice on pathogen competition or strain invasion for vaccine-preventable infectious diseases. Coupling game dynamic framework of vaccination choice and compartmental disease transmission model of two strains, we explore invasion and persistence of a mutant in the population despite having a lower reproduction rate than the resident one. We illustrate that higher perceived strain severity and lower perceived vaccine efficacy are necessary conditions for the persistence of a mutant strain. The numerical simulation also extends these invasion and persistence analyses under asymmetric cross-protective immunity of these strains. We show that the dynamics of this cross-immunity model under human vaccination choices is determined by the interplay of parameters defining the cross-immune response function, perceived risk of infection, and vaccine efficacy, and it can exhibit invasion and persistence of mutant strain, even complete exclusion of resident strain in the regime of sufficiently high perceived risk. We conclude by discussing public health implications of the results, that proper risk communication in public about the severity of the disease is an important task to reduce the chance of mutant invasion. Thus, understanding pathogen competitions under social interactions and choices may be an important component for policymakers for strategic decision-making. © 2021 Elsevier Inc.