Over the holiday break, I took advantage of the downtime to finally do some reading. I skew towards non-fiction and found a lightweight book on game theory that refreshed my thinking on a fascinating course I took 20 years ago.

Thus primed, when following the news on COVID-19 and individuals’ responses to social distancing, it dawned on me that the choice to follow mandates or ignore them was a version of the prisoner’s dilemma. I decided to explore this a bit further with a basic scenario.

Scenario

For this prisoner’s dilemma scenario, let’s imagine our two players live in a city where COVID-19 rates have been increasing. The mayor has closed most business and put in place a stay-at-home advisory–but not an order–for the next three weeks. Players must decide between going out and socializing with friends or sitting on their couch and watching Netflix.

If both players stay at home during those three weeks, the COVID-19 rate drops and the advisory is lifted, and gyms and restaurants reopen. If both players goes out, the COVID-19 rate spikes and the advisory will move to a strictly enforced lockdown for three weeks. If only one player goes out, they get to experience the fun of a night out, but the advisory is extended for an additional three weeks.

The Payoff Matrix

Let’s assign values for each outcome. We’ll start with both individuals staying home. It’s not fun staying at home, but the upside is the advisory gets lifted. Both players get a value of 5.

If one individual goes out, they get the benefit of going out, which keeps their spirits up through the additional three weeks of the stay-at-home advisor. Let’s say this is value of 8. For the individual who stayed home, they are regretting their decision as they’re stuck at home for another three weeks. This is value 0.

If both individuals go out, they get to experience the joy of a night out, but then will be stuck at home for a while. In this outcome, both players have value 3.

We’re making generous assumptions and simplifications here.

The Result

Neither player knows what the other will choose. However, they can see that the value to them of going out is always better than the value of staying in. As a result, both players choose to go out, and now they’re stuck at home for three more weeks. The diagram below shows this outcome, and the cell in orange is considered the Nash equilibrium for this game.

The Payoff Matrix for the COVID-19 Prisoner's Dilemma shows that individuals will choose to "defect" and reach a sub-optimal game state

The key takeaway is that even though both parties staying at home yields the best outcome, this won’t happen if players are acting rationally and trying to maximize their own payoff.

Conclusion

This was a contrived example that simplified the decision and dynamic, and also modeled the question on whether to stay home as a two-person game. But it shows how rational self-interest can lead to sub-optimal outcomes for society.

Others have written about COVID-19 and the prisoner’s dilemma, some far before the thought crossed my mind. Other scenarios explored include individuals stockpiling groceries, individuals deciding whether to get vaccinated, whether states cooperate on COVID-19 restrictions, and how vaccines are allocated between countries.

Each of these scenarios show the challenges in getting actors to cooperate for mutual benefit–it’s all too tempting to defect and secure the best individual outcome for oneself.