The Tragedy of the Commons: Game Theory and the Novel Coronavirus
The unprecedented nature of the global pandemic has been new and challenging. In many ways, COVID-19 has necessitated individuals to “do our part” and forgo many pleasurable past-times and activities that may propagate the spread of the virus. Practicing good social distancing, wearing masks, and washing hands are all great ways to reduce our risk of transmitting and receiving the virus. This is done to prevent overwhelming hospitals and ensuring that those individuals who are more vulnerable, such as the elderly and those with pre-existing conditions, are able to be treated. Indeed, if we were to think radically, we could all simply isolate for two weeks and eradicate the disease in its entirety. However, this is not the way the world works. Sadly, time and time again, we see that individuals are not motivated by what serves the collective good, but rather seek to selfishly gain their best outcome.
Ronald Bailey’s article critiques how many, particular young people such as ourselves, are facilitating the spread of this pandemic by recklessly prioritising our own self-interests:
Through actions that are probably low-risk for young and healthy individuals, such as going to bars and socialising in large groups, we can exponentially increase community infections and contribute to the death of others. Such a situation, in which shared resources such as streets and public places are exploited by people not practicing mask-wearing or distancing, is a type of tragedy of the commons. Here, selfish individuals cause a worst outcome for everyone!
We have learned of a somewhat similar situation in this course, known as Braess’s paradox.
Consider this graphic of a road network, taken from Wikipedia:
Here the roads from S -> E and B -> E have travel time T/100 where T is the number of cars on that road at the given time. The Roads S -> B and A -> E have constant travel time of 45.
Now, let’s consider when there are 4000 cars. Any rational driver wishes to take the shortest route possible. As there are just two routes: S -> B -> E and S -> A -> E we know that the cars will reach an equilibrium when travel time of each route is equal.
Letting S -> A have a cars and B -> E have b cars
We know: a/100 + 45 = 45 + b/100 and A + B = 4000. Hence, A = B = 2000 is the solution.
So each car, in equilibrium, takes 65 mins to reach destination.
And now we introduce a magical new road A -> B that takes zero minutes! Even if all the cars take S -> A -> B, this will at worst take 4000/100 = 40 mins < 45 mins = S -> B. And so every car either takes S -> A -> E or S -> A -> B -> E. But now we note that B -> E similarly will always outperform A -> E at a max of 40 mins, even at peak t of 4000. So all rational and selfish cars take a route S -> A -> B -> E which takes a total of 4000/100 + 0 + 4000/100 = 80 mins. Somehow, adding a road actually increased the travel time for everyone!
That is fascinating, but how does this relate to the Coronavirus you ask?
Braess’s Paradox is a remarkable example of the tragedy of the commons, showing us how being selfish can often lead to a worst outcome for everyone! Because no car cares about attaining the socially optimum solution, which in this case could be considered the average travel time over the road network, everyone suffers.
For instance, if just 500 cars took S -> B -> E (1) and another 500 took S -> A -> E (2). Group (1) would take 3500/100 + 45 = 80 mins and Group (2) would take 45 + 3500/100 = 80 mins but the other 3000 cars would take 3500/100 + 3500/100 = 70 mins
This brings the average travel time to (70 * 3900 + 100 * 2 * 80)/4000 = 72.25 mins. So we can get a better outcome for everyone if individuals choose to care for others and behave for the collective good! We shouldn’t be like selfish car drivers, spreading COVID in pursuit of our own enjoyment and pleasure, but try work together to create a better outcome for everyone!
This Can be Illustrated Through a Very Simply Game:
| Student on Right ->
Immunocompromised and Elderly Professor Along Rows
|
Go to Supermarket with Mask | Go to Supermarket without mask |
| Stay at Home
|
-100, 100 | -100, 120 |
| Go to Supermarket with Mask | 100, 100 | 5, 120 |
Suppose you are a student (who already has antibodies) and want to go buy groceries. A dominant strategy for you (one in which you always gains the most value) is going to the supermarket without a mask. This is because, you have low risk, and find the masks uncomfortable. Yet in doing so, you endanger the immunocompromised professor who has no choice but to choose to go to the supermarket, as that is a better option than staying at home and having no food. So 5,120 forms a Nash Equilibrium. This provides an average reward of 62.5, because the professor isn’t gaining much value due to the increased risk of exposure, but has no better response.
The socially optimum response, off course, is both players going to the supermarket and buying what they need with masks. Here, both players gain an average reward of 100, almost twice as much!
So the moral is: Don’t be a selfish player in a system! Think about the other players in the game! Work together to reach social optimums instead of settling mindlessly into a harmful Nash Equilibrium.