We study a game-theoretic model in which there are two periods of time in each of which agents (players) make a vaccination decision, and they choose the level of economic activities. In addition, we consider two kinds of policy measures 1) a vaccination passport policy and 2) a subsidy policy to promote vaccination, and compare the social welfare in each case. We find that introducing a vaccine passport policy or subsidizing to mitigate the expected costs from vaccination may decrease the social welfare when a vaccine is effective to reducing the extent of severeness of illness from virus infection but not successful in curbing the transmissibility of virus.