Social Distancing and Game Theory

Introduction

To go out or not to go out, that is the question. For 2 years, we had lockdowns, cancellations, vaccinations and boosters, all for preventing the spread and severity COVID-19. However, as humans do, we will all need to go out eventually, so people during this time had to decide whether the risk of getting COVID-19 while going outside was worth it. We will be looking at examples where game theory is applied to best model the pandemic.

Evolutionary Game Theory

In class, we have only focused on Game Theory in the context that players want to maximize a payoff after choosing a strategy. Strategies are played simultaneously, with players being unable to coordinate among themselves. Evolutionary Game Theory is similar, with strategies being played among players over time, which typically affects the payoff. This is where the evolution part of Evolutionary Game Theory comes from, and unlike in regular Game Theory, Evolutionary Game Theory can allow for players to play different strategies at different times.

Modelling the Pandemic

As described in the paper, a way of modelling this problem is with Evolutionary Game Theory. This would contain 2 strategies, where each individual can do one of the following:

• Strategy A: Social distancing and only contacting with housemates.
• Strategy B: Not respecting social distancing guidelines.

How payoff, which is what each player wants to maximize, is calculated in this model is dependant on time, and how many are diseased in each group at that current time frame. There are also constants like transmission rate and reproduction rate of the virus.

After performing simulations with the model, we were able to conclude the following relations between the populations that socially distance versus those who do not, with beta being the transmission rate and R being the virus reproduction numbers:

In this game, we also know that there are equilibriums, given certain constraints. Here is a trivial example; if there is no disease at all, then both players are at equilibrium regardless of which strategy. This is due to how that there are no viruses, no one would get infected regardless of which strategy they take.

Conclusion

While this is a good model on how a virus could spread to those who distance themselves vs. those do not, there are other attributes we can consider that can help with making the model more realistic with the COVID-19 pandemic. For example, having 2 strategies assumes that these populations consistently follow social distancing guidelines may not be a good assumption, as people could more or less follow them in between of following them always and not following them at all. Another aspect we can factor into when considering the payoff values is vaccination which can decrease the likelihood of being infected.

Sources:

• https://plato.stanford.edu/entries/game-evolutionary/
• https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1000793