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The Game Theory of Masks

I see a lot people mocking the CDC’s guidance to remain masked and social distanced even after vaccination. Obviously the point of vaccinations is not to have to take those precautionary measures. But what the CDC is probably doing is thinking about this game of imperfect information. If someone says they are vaccinated, you have no good way of knowing that, so there is a free rider problem. In game theory, there is a way of visualizing the incentives that guide the players.