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How important is social distancing nowadays? Analyzed using game theory

Introduction

 Outbreak and spread of Corona Virus is rising as one of the most concerned and controversial issues from all around the world. 

This data from the WHO shows the exponential growth of confirmed corona virus cases in United States, and this trend is anticipated to continue for next few weeks.

In their desperate efforts to slow down the spread of Corona virus, majority of the countries have mandated social distancing as a primary measure against it.

Corona Virus and mandated social distancing in response to Corona Virus has been damaging almost every aspects of human life as well as activities: world economy is shrinking, unemployment level is increasing, public schools and institutions has shut down, and health care facilities are overloaded with skyrocketing number of Corona Virus patients.

This data from US Bureau of Labor Statistics reveals the enormous number of people losing their job as a result of corona outbreak and the government’s responsive social distancing policy against it.

As an empathy interview, I have interviewed my father who is working as a business man in India to give a comment about his honest opinions about this situation as a businessman and individual.

He answered that there is no doubt that social distancing is unpleasant as well as discomfortable. As a result of lock down policy in India, he could no longer continue to work in his office and thus his revenue has decreased for more than 50% in past few month. In addition, his commented that his standard of living has significantly decreased as his freedom to go out is prohibited and thus there are limited amount of activities to deal with his boredom. 

Given the statistics and interview from my father, it apparent that social distancing policy entails a large number of significant consequences for individuals as well as countries. Considering these drawbacks, would social distancing policy be truly necessary and beneficial?

In this project, I will investigate the underestimated significance of social distancing using game theory model.

 

The game theory model

Players and their strategies

The players are the country and individuals in that country.

The country has three strategies: mandating social distancing one day, two day, and three days after the first confirmed case appear in the country.

The individuals in the country will have two strategies: obeying the policy and staying at home, ignoring the policy and refraining from social distancing. For simplicity, I would assume that all individuals in the country act same as one another. So, if the strategy chosen by the individual is ignoring the policy, all of the individuals in the country will ignore the policy.

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

Outcomes

There are six possible outcomes of the game:

A:Government mandate social distancing one day after the first confirmed case and individuals obey the policy

B:Government mandate social distancing one day after the first confirmed case and individuals ignore the policy

C:Government mandate social distancing two day after the first confirmed case and individuals obey the policy

D:Government mandate social distancing two day after the first confirmed case and individuals ignore the policy

E:Government mandate social distancing three day after the first confirmed case and individuals obey the policy

F:Government mandate social distancing three day after the first confirmed case and individuals ignore the policy

Payoffs

Payoffs for the country

Payoff is basically a benefit or a lose for the player. If the higher the value, the more beneficial it is for the player.

Here, for every six of the outcomes, we must assign payoffs for both players of the game.

First, let’s find out how social distancing can be important for the country and individuals.

According to the model established by the Center for Disease Control and Prevention, by implementing the social distancing policy, the country can reduce the maximum daily number of cases. This will allow the health care institutions not to be overwhelmed by the overflow of the patients and prepare the equipment for more patients.

Also, according to this epidemiological model visualized by New York Times shows that the earlier the date of obligation of social distancing, the less cumulative cases for Corona Virus. Based on this model, we can figure out that the the maximum number of cases when social distancing was implemented on day n+1 is 40% more than the maximum number of cases when social distancing was implemented on day n.

Assuming that this holds true in the country of our game, let’s assume that the payoff for country to mandate social distancing one day after the first case is confirmed is -10. Then the payoff for country to mandate social distancing two days after will be 40% worse, which will be -14. The same rule will apply to the last strategy of the country and thus the payoff of it will be -(14)x1.4=about -20.

Payoffs for the individuals

Now lets look at the payoff for individuals. If the individuals choose to obey the policy they would feel uncomfortable and possible face significant decrease in income, or even lose job in unfortunate cases. Hence, the payoff for choosing to obey will be about -5 for individuals.

If the individuals chooses to disobey the policy, they would feel better, but there will be a higher possibility of getting the Virus. So the reasonable payoff for individuals in this case will be about -3. In this case, the country will also be harmed as disobeying social distancing can expedite spread the virus. Hence, in this case, the country will also be harmed and thus there will be additional payoff of about -5 for the country.

There is another factor that can affect the well being of the individuals: the country. Since well being of individuals depends on the well being of the country, the payoffs for the country will be added to the payoff of the individuals.

Overall payoffs for each of the outcomes

Let’s get back to our matrix game.

Given the payoff rules in the previous paragraphs, I will assign the payoff of both players for each of the outcomes. Payoff will be notated in format of (payoff for individuals, payoff for country)

Outcome A:(-15,-10)

Outcome B:(-18,-15)

Outcome C:(-19,-14)

Outcome D:(-22,-19)

Outcome E:(-25,-20)

Outcome F:(-28,-25)

Solving the game using movement diagram

With the assigned payoffs, we can put numbers into each of the outcomes.

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

In this case, the Nash Equilibrium is the squared outcome where the government mandates social distancing one day after the confirmed case of corona virus appeared, and individuals chose to obey social distancing policy.

We will also find what is called Pareto Optimal Outcome. This outcome refers to the best outcome for both players: individuals and country. We find this outcome by plotting data points in the x-y plane having x value as the payoff of individuals and y values as payoff of the country. The point at the upper right side of the plane is the Pareto Optimal Outcome.

Since, the outcome A where payoff is (-15,-10) is at the upper right side of the plane, this outcome is Pareto Optimal Outcome. Since both Nash Equilibrium and Pareto Optimal Outcome is same, this outcome is the solution to this game. Our best outcome will be when the country mandate social distancing as soon as possible and when the individuals in the country obeys to this policy.

So what can we do in response to this issue?

In conclusions, although social distancing policies, such as shutting down of schools and country-wide lock downs, seem like a overreaction of the government, the benefit of this policy far outweighs the consequences in terms of long term benefit of the country and individuals. Given that social distancing is the best out of worst options against this situation, we must understand the importance of social distancing and keep practicing it to make small contribution to our respective countries. It is the sum of small contributions from all of you that makes the large changes in our society!

Reference Pages

https://www.vox.com/2020/3/15/21180342/coronavirus-covid-19-us-social-distancing

https://www.forbes.com/sites/startswithabang/2020/03/17/why-exponential-growth-is-so-scary-for-the-covid-19-coronavirus/#4bb9fbe94e9b

https://economictimes.indiatimes.com/news/politics-and-nation/heres-what-social-distancing-entails/orders-from-the-centre/slideshow/74704858.cms

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COMMENTS: 4
  1. April 26, 2020 by Shari Abbott

    Sunki, I enjoyed the layout of your presentation. Although you had no video, the clear, straightforward language and sentences made this a clear and easy to understand read, even for someone like me with little understanding of Game Theory. Your dad’s insights were interesting and I wanted to know more about his views based upon long and short term distancing, like your questions asked. I also found your argument compelling, as you explained both the graphing as well as the significances of the conclusions. As your former English teacher, I know you know how to cite in MLA! URLs do not cut it. But that aside, thanks for such a strong explanation.

  2. April 26, 2020 by Pranav Unni

    Sunki, I really like the way the page has been done. The information is well-thought-out and clear which made it is easier for me to understand how exactly you used Game Theory to analyze the situation. I think that the visual elements used to aid the overall page makes it easier to understand the process of using Game Theory. Great job!

  3. April 26, 2020 by Harish

    Hi Sunki, you’re graphs and tables are very clear and are easy to understand. You’re rationale for the payoffs makes sense to me. I think everything ties in well as a story. Well Done!!!

  4. April 27, 2020 by Emmy

    H Sunki! I really enjoyed your use of images coupled with great explanations, I have personally never taken Game Theory but your explanations just made sense to me. I also love how you applied this to an event that is happening in our world today!

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