A Game Theory Approach to Covid-19 Guidelines
A Game Theory Approach to Covid-19 Guidelines
I will offer a disclaimer here, I am not a doctor, and none of this is medical advice.
Current Covid-19 guidelines leave students at Cornell with a few decisions to be made. The first is to socially distance and isolate completely. While this decision would not have an immediate payoff, the payoff for the community as a whole is increased greatly if this is followed. The second decision is to commit to a reasonable amount of isolation. This would have an increased immediate payoff, but a decreased total payoff for the community. Finally, there is the decision to refuse to distance and isolate at all, with the highest payoff for the self, but the lowest community payoff.
Let’s construct a very basic model for this game. The community payoff is added to (or subtracted from) the payoffs of each of the members, and is calculated from the number of players making each decision. While the players are aware of the community payoff, however, they cannot see what decisions the other players are making. I won’t discuss the actual payoffs and penalties, that would be a much better job for a sociologist or an epidemiologist.
While I think this game would be too complex to look into with my elementary knowledge of Game Theory, I do think that we can still glean a bit from this model.
The most elementary conclusion is that if everyone acts in self interest, and optimizes their immediate payoff, and not the community payoff, then there will be disastrous consequences for the community. This would result in everyone not being responsible and distanced.
The other two decisions that people can make offer much better outcomes for the community. However, what we probably see now in the real world is a mixture of all three decisions. A few people are probably choosing to isolate severely or not at all, while the vast majority are maintaining a medium level of isolation. (This discussion of levels begs the question of whether discrete levels of isolation are too much of a simplification. Levels of isolation are probably more continuous among the population. Perhaps they follow a known distribution?)
Looking back to the game model, medium isolation is probably the rational decision to make, optimizing both the community payoffs, as well as the immediate self payoff. But this general case is very general. Perhaps as the course progresses, we will be able to answer more of these questions with greater detail.
What we could look at is a simple game of a two person interaction with two actions: mask on or mask off. If both players keep the mask on, then the payoff might be slightly negative. Wearing a mask is uncomfortable and undesirable. If one person wears the mask, while the other doesn’t, both people are probably safe from covid, and so the person not wearing the mask benefits slightly. But if both masks are not worn, then both players have a larger negative payoff, the consequence of Covid.
This looks a lot like the prisoner’s dilemma! However, the payoffs are slightly different. Let’s draw the graph for it below:
| Player 2 | |||
| Player 1 | Mask On | Mask Off | |
| Mask On | (-1, -1) | (-1, 0) | |
| Mask Off | (0, -1) | (-5, -5) | |
There is no pure Nash Equilibrium here. If we consider the game from Player 1’s point of view, if Player 2 removes their mask, then the rational Player 1 should keep it on. If Player two keeps their mask on, then the rational Player 1 would take their mask off. What if both players were vaccinated, and the payoff for not masking is no longer negative?
| Player 2 | |||
| Player 1 | Mask On | Mask Off | |
| Mask On | (-1, -1) | (-1, 0) | |
| Mask Off | (0, -1) | (0, 0) | |
Here, there is clearly a Nash Equilibrium with a mutually dominant strategy of taking the mask off.
And what if the players were not vaccinated, and masks were not 100% effective. Now the payoff for not wearing a mask is worse than the tradeoff for wearing one.
| Player 2 | |||
| Player 1 | Mask On | Mask Off | |
| Mask On | (-1, -1) | (-1, -2) | |
| Mask Off | (-2, -1) | (-5, -5) | |
Now the Nash Equilibrium has flipped, the mutually dominant strategy is to wear a mask!
It is very interesting to play with the parameters of the model to see how different players would act in different situations. Maybe Player 1 has a preexisting condition and has a very negative payoff if they catch covid! Maybe both players are in a romantic relationship, and have a very positive payoff for keeping the mask off! Game theory allows us to analyze many different scenarios and see how different players would act.
And of course, this capability has not gone unnoticed, with researchers using games to analyze many different aspects of the pandemic, from providing pandemic care to whether or not people will get vaccinations. More information on that can be found here: https://www.rand.org/blog/2021/03/how-game-theory-could-solve-the-covid-19-vaccine-rollout.html.
Happy gaming!