Game Theory Can Explain Why You Should Wear A Mask

The prisoner’s dilemma is one of the most famous examples of game theory, which is the study of how two parties interact and determine strategies in competitive environments. 

In this game, two apprehended bank robbers (Brendan and Jackson) have been placed in separate rooms so that they cannot communicate with each other. Each has two options: to confess or to remain silent. If Brendan and Jackson remain silent, they each get a 2-year sentence. However, if Brendan confesses while Jackson remains silent, then Brendan will only get a 1-year sentence while Jackson receives an 8-year sentence. And vice versa. If both confess, both receive a 5-year sentence. The model below visually represents this game. 

Clearly, the optimal outcome is if both prisoners remain silent. However, there’s a paradox, as both Brendan and Jackson are inclined to confess. They may be motivated to receive the 1-year sentence. Or they both fear the result of getting 8 years if their partner confesses. As a result, both confess and receive 5 years — not the optimal outcome.

The prisoner’s dilemma demonstrates how choosing the best outcome for an individual may create a less than optimal outcome overall. And this is often true in the real world, where a lack of cooperation can lead to an inefficient outcome overall. 

Game theory can help model the decision to wear a mask. Interestingly, we can even model these decisions under different assumptions that reflect the reasons (albeit incorrect) for not wearing a mask. 

Let’s define the players of this game as two individuals who have to make the decision of whether they want to wear a mask or not when going out. Like any decision, this decision depends on how the individual evaluates his/her costs (discomfort, ‘loss of freedom’) and benefits (reduced risk of infection, social approval).⁵

Many believe that masks only protect others and that they offer no self-protection. If this were true, an individual would only receive the health benefits of masks if others around them wore one. This is a common misconception as it is closest to the current scientific understanding of how masks work (to be clear however, science has shown that masks also protect the wearer to a certain extent).

This becomes a paradox that resembles the prisoner’s dilemma. An individual with this belief may act in self-interest and not wear a mask to avoid the discomfort and still receive the health benefits. However, there are likely many others with this belief that may make the same self-interested decision. As a result of this non-cooperation, both players choose to not wear a mask and end up suffering. 

The model above visually represents this. The health benefit of the other individual wearing a mask was arbitrarily assigned a value of 10. The cost of wearing the mask was arbitrarily assigned a value of -2. While the most efficient outcome is to have both individuals wear a mask (8,8), the end outcome is actually (0,0). 

This model is very similar and equally works to represent the belief set that masks only work when both parties wear one.

People with this belief set argue that they should have the liberty to risk their own health. For example, I came across one poster held by a protester that read:

“If you’re wearing a mask, why would you care if I’m not? Your mask works, right?”

Of course, this is not how the virus works — by electing to not wear a mask, you are also risking others’ lives. Nevertheless, let’s structure our model around this belief set to see if cooperation results in the most efficient outcome, regardless of this belief’s accuracy. 

In the above model, individuals who don’t want to wear masks clearly believe that the benefits of not wearing a mask (avoiding the discomfort and feeling ‘free’) outweigh the potential health consequences. Therefore, we need to readjust the values we assign. We can do this by negating the values so that the cost is greater than the benefit. For example, the benefit of wearing a mask can equal 2 and the cost of wearing a mask can equal -10.

Based on this, the optimal outcome for both individuals would be to not wear a mask. This is the outcome that provides the highest utility to both individuals separately and as a group. 

However, translating this to the real world shows that this might not necessarily be the case.

While the immediate cost of not wearing a mask may be a negative impact on your health, the pandemic continues to surge when a large number of people choose this route. As a result, your favorite restaurant may remain take-out only. You’ll continually abide by the mandatory mask restrictions at stores and buildings. NFL football remains closed. Paradoxical, isn’t it?

It is important to recognize that there are other players besides just individuals such as public/private entities who make decisions based on the statistics of the pandemic. As a result, our costs and benefits are not limited to the short term, and we may be blindsided by present bias. This makes a strong case for why cooperating and wearing a mask might, in fact, be the highest utility outcome. 

Yes, some people still don’t believe that the coronavirus really exists, or that it is not dangerous. This results in the decision to not wear a mask. Similarly, those that believe that masks offer no protection whatsoever will also decide to not wear a mask. In such cases, the perceived benefit (mask’s effectiveness) of wearing a mask is 0, and the cost (discomfort) of wearing the mask is still -2.

If these incorrect beliefs happened to be true, then the optimal outcome for society would be to not wear a mask, right? Well, it’s not that simple. Masks are more than just protective gear — they are a signal of cooperation and responsibility. While some individuals may believe that masks are not protective, others still do. In fact, most Americans do believe that the pandemic is dangerous, regardless of whether it actually is or isn’t. So how does this affect society?

Let’s consider the economy. During the initial shutdowns, US consumer spending significantly decreased.  After re-opening the economy, spending increased again, but not quite to its original levels. Even a 10% decrease from the baseline spending levels can spell out an economic catastrophe characterized by high unemployment and recession. 

One contributing factor to why spending hasn’t returned back to normal is because many people are still concerned about the dangers of the virus. This may be due to the fact that people still see many others deciding not to wear a mask.

And thus, cooperation again results in an optimal outcome for society, even when we disregard any of the ‘controversial’ beliefs around the health dangers of the virus or the effectiveness of wearing a mask. Reopening the economy only works if everyone is convinced that it really is safe to go outside. By not wearing a mask, you send the opposite signal, thereby depressing the economy by persuading others to stay inside. 

Game theory shows us that, regardless of what an individual believes, it is in their own self-interest to wear a mask.

While the conflict surrounding wearing masks will persist, these insights shed light on a new perspective on the benefits of wearing masks during this time, even outside the realm of public health and science. Next time you encounter a family member, friend, co-worker, or even a stranger who is against wearing masks, consider explaining that their decision, although self-interested in the short-run, only hurts them in the long run.

Just like in the prisoner’s dilemma, cooperation results in the most efficient outcome. If we cooperate and wear masks, the pandemic will be better mitigated and we may finally find true freedom again.