How Can Game Theory Be Used to Discuss Strategy Toward COVID-19?

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My intro video!

What is the problem?

We will remember 2020 as the year we were hit by a previously unknown and remorseless foe. Nowadays, COVID-19 is the most important problem that people are struggling with. Coronavirus is killing thousands of people per day, so it is a crucial topic that we need to pay enough attention to it. The pandemic’s economic impact continues to be closely related to the severity of the public health crisis, as governments are forced to restrict public life and economic activity when capacity within healthcare systems is reached or exceeded. Government protection of the population resulting in lower deaths per capita helps to cushion economic decline; therefore, the strategy that governments choose can have a massive impact.


THE GAME THEORY MODEL:

PLAYERS AND THEIR STRATEGIES

The game theory looks at strategic interactions between rational people and mathematically models what their interactions might look like.

Despite the repeated consensus that adhering to social distancing guidelines is the most effective way to diffuse the novel coronavirus pandemic, some people tend to break quarantine and go out for different reasons. Now I want to examine this problem through the lens of Game theory!

Who are the players? In this game we have two players; you and others in your community.

What are the strategies? You are you, and the ‘Others’ are the people in your community, workplace, class, etc. You both have the same set of decisions or strategies available to you: Stay In (quarantine) or Go Out (don’t quarantine). The combinations of the different strategies you both choose results in four different payoffs:

We can model the decision to quarantine/go out with the following matrix:

OUTCOMES and payoffs:

(These outcomes represent months of utility)

A: If You and the Others choose to Stay In, (i.e. everyone quarantines) both parties lose only one (-1) because we all flatten the curve and find a solution faster.

B: If You join the Dark Side and Go Out, you lose 0 MOU (months of utility). While everyone else is stuck at home, you gain an edge over your competitors in your class, workplace, community, etc. Sans competition, you become hyper-productive and squeeze 2 MOU out of your time, putting you ahead of the Others.
The Others could have done this as well but chose not to, so this represents a 2-month opportunity cost on top of the 1 month they’re losing because of quarantine, putting the Others’ payoff at -3.

C: The same principle applies in reverse. If You Stay In while the Others Go Out, they lose 0 MOU and you get a -3 payoff.

D: If both parties Go Out, (no one quarantines), then the virus spreads quicker and the government enforces a longer quarantine: everyone loses 2 

Here, we can draw what’s called a movement diagram that shows the strategy that each player prefers. If both players prefer the same outcome, they will reach what is called Nash Equilibrium.

A Nash Equilibrium in game theory is a collection of strategies, one for each player in a social game, where there is no benefit for any player to switch strategies. In this situation, all players in the game are satisfied with their game choices at the same time, so the game remains at equilibrium. (More information)

(-2, -2) is the Nash Equilibrium”

Eventually, both You and the Others decide to Go Out, resulting in the worst possible payoff (-2,-2) — the infection spreads, and we all have to spend more time in quarantine.
This is a Prisoner’s Dilemma game, and logical thinking from both parties will always result in a globally inferior Nash equilibrium (both players Go Out, which sucks for everybody). (Prisoner’s Dilemma game)
People are choosing not to quarantine because, from their positions, it’s the most rational thing to do.
But no one is perfectly rational, and I doubt every non-quarantiner goes through this thought process when they decide to leave the house.


What governments need to do?

COVID-19 is no longer a battle against a virus. It is also a battle within society against the uncooperative. In this situation, people tend to go out and break quarantine. Governments should find the best strategy to control this pandemic because if it becomes out of control, it will have irrecoverable outcomes. I tried to examine strategies that government may plan to control the pandemic and prevent economic decline. Finally, I’m going to find the strategy that would have the best outcome for everyone!

Who are the players? In this game, we also have two players; country (government) and individuals in that country.

What are the strategies?

The country has three strategies:
1) Strict lockdown, with paying salaries, and fining people who break quarantine.
2) Mild lockdown and fining people who break quarantine ( but less than before)
3) Don’t quarantine

The individuals in the country will have two strategies:
1) Obeying the protocols and staying at home
2) Ignoring the policy and go out.
(For simplicity, I would assume that all individuals in the country act the same as one another.)

Then, we can create the following 2×3 matrix game:

OUTCOMES AND PAYOFFS:

Now we are going to determine each outcome, but before that, we should know some facts!

  • Since people tend to go out because they think they will gain an edge over their competitors in their class, workplace, community, etc., therefore, the payoff for going out is +1. Those people who are stuck at home get 0 points.
  • In terms of salary, whenever government pays the salary, they will gain 2 points (+2), and the government loses 2 points (-2).
  • However, people who break quarantine will fine. In a strict lockdown, they lose 3 points (-3), and governments get 2 points (+2) but in mild lockdown, quarantine breakers lose 2 (-2) and governments get 1 point (+1).
  • In terms of controlling the pandemic when it is a strict lockdown, spreading the virus gets slower, and the government will gain 3 points (+3) because they controlled the pandemic.
  • When it is a mild lockdown, the government will gain 0 points, and when it’s not quarantine, they will lose 2 points (-2) because the virus gets out of control.

A= When the government announces strict lockdown and people obey, people who obey get 2 points ( 0+2=2), and the government gains 1 point (3-2=1).

B= When the government announces mild lockdown, and people obey, people who obey get 0 points, and the government gains 0 points as well!

C= When there is no quarantine, people who stay at home get 0 points, and the government loses 2 points (-2) because of spreading the virus.

D= When the government announces strict lockdown, and people ignore it, people get 0 (1+2-3=0), and the government gain 3 points (-2+2-+3=3)

E= When the government announces mild lockdown, and people ignore it, people lose one point (-2+1=-1), and the government gain one point (1+0=1)

F= When there is no quarantine, people who go out get 1 point (+1), and the government loses 2 points (-2) because of spreading the virus.

Here, we can draw a movement diagram that shows the strategy that each player prefers. If both players prefer the same outcome, they will reach Nash Equilibrium.

“(2,1) is the Nash Equilibrium”

MY RESPONSE: WHAT IS THE BEST STRATEGY?

As we learned through modeling the situation, people tend to go out
Hence, governments’ crucial challenge is to make people stay at home, so they need to find a strategy to control the pandemic and prevent economic decline. The country that does both of them in the best way can be the winner of this cruel and challenging game!

Then I tried to model the second situation to find the best strategy for both people and governments. Finally, I found out strict lockdown( when government also pay salary and fine people who break the quarantine) would be the best strategy for the government and also it can make people stay at home!


FEEDBACK:

Thanks for reading! I would love to hear your feedback, so please leave a note in the comments section below! In addition, I’d appreciate it if you could answer these questions:

  • What other strategies do you think can help governments to control the pandemic?
  • Wich part of the website was interesting to you?
  • What can I do or change to make this website better?

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