Question

Corona: Suppose that all people can transmit the corona virus with a certain probability p to another person without knowing it. Furthermore, assume that wearing a face mask reduces the probability that you transmit the virus to another person to zero but does nothing to protect yourself (both of these assumptions are not true in reality). Catching the virus with probability p gives you a payoff of -100 * p. Wearing a face mask is obviously inconvenient and reduces your payoff by 10.

1. Model the situation as a simultaneous 2 person game.

2. What is the game theoretic prediction and why?

3. What would help in this situation?

Answer 1

		Person 2
		Wear A Mask	Don't Wear a Mask
Person 1	Wear a Mask	-10,-10	-10-100p,0
Don't Wear a Mask	0,-10-100p	-100p,-100p

We see that for each person, not wearing a mask leads to a higher payoff than wearing a mask irrespective of the strategy of the other player. So that is the dominant strategy for each player. Thus the theoretic prediction will be that none of the people wear a mask.

In this situation, we see that if both people wear a mask, the payoff is better than the case if both do not wear a mask if p >0.1 which is in all likelihood the case. So there should be a punishment for not wearing the mask in general when the people who do not wear a mask should have to pay a fine for which the utility loss should be more than 10. As a result, Wearing a mask would become the dominant strategy and thus everyone will wear a mask.

The other thing that can be done is if the people wearing a mask are incentivized so as to ensure that they get a value of more than 10. But that would be difficult to administer and much more costly for the authorities. So it better to penalize offenders than incentivizing followers.

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