Introductory Video

Why did I choose this topic?

To me, this problem is important because my family has been personally struggling with whether to attend school or not in these trying times, especially when hearing about stories of high-schoolers getting the disease both in our school as well as secondary schools around the country. As a result, I wanted to make a game theory project modelling to determine the best course of action that governments, the educational system (i.e. school boards and provincial/state governments), and individual families should take in this scenario. This is important now more than ever due to the findings of new variants that have popped up around the world and their potential to wreak more havoc than ever before. On the other hand, there are real concerns surrounding the efficacy of online schooling as well as income inequality. Should we go back and re-enter a lockdown in which schools are closed in order to more effectively combat the virus? Or should we leave them open to stop other societal concerns from occurring?

Learning Online: Problems and Solutions | UNICEF North Macedonia
Student experiencing technical difficulties on online schooling. Source: UNICEF

Summary of the Problem

Since the outbreak of the coronavirus, there has always been a question of whether schools should be closed. Schools are natural breeding grounds for COVID-19, given that many students are unwilling to follow restrictions and the density of students within an enclosed environment. While younger students are less prone to the deadly symptoms of COVID, they can still fall seriously ill, and more importantly, are effective transmitters of the disease to other people in the family and the community as a whole. This is especially important considering that there is a disproportionate amount of young people who are not fully following COVID restrictions and are still going out to parties and visiting large groups of friends. However, research about this is somewhat divided. In fact, according to some studies by the CDC, the risk of transmission in schools is not significantly higher than that in the community. Many areas of the world last year have already closed down their schooling systems temporarily, and some parts of the world as still pursuing either full closures or a hybrid system. Where I live, in Canada, schools are open. There are legitimate arguments to be made on both sides. As I can testify to, online schooling is significantly less effective than in-person schooling. This is due to distractions, technical issues, and even inexperience for teachers who are teaching in an unfamiliar platform. Further, for those under the poverty line, school closures can exacerbate food insecurity and increase the gaps in education between poorer students (who don’t have access to tutors or the latest computer technology) and wealthier ones. There are also issues surrounding mental health and isolation for children. On the other hand, arguments have been made in favour of school closures due to the potential of outbreaks that can exist in order to flatten the curve. Further, there is an argument that opening schools allow for COVID to spread in the short run mean that schools will have to be closed in either scenario, albeit for a longer period of time.

School closures are not without precedent. In March 2020, about 150 countries fully closed their schools and 10 more partially closed them. Even now, countries around the world are opting to keep schools closed or partially closed in order to limit the spread of COVID-19.

Differences in school closure policy around the world. Source: UNESCO


Setup of the game

Shown below is a sequential model of the game that I have created. The first player is the government, who decides what policy to make for the economy as a whole: either staying open or entering lockdown. Then, regional school boards decide whether to stay open or to shift toward online schooling instead. Finally, families can choose either to go to school or pursuing an online option. I believe that a sequential model fits this situation very well since these decisions are not made at the same time but instead are made one after the other. Note that when school boards choose online schooling, families have no choice but to follow the online schooling option since going to school is impossible. 

What do each of the decisions mean?


Stay open – the government imposes little to no restrictions at all. They only send out awareness campaigns about COVID and advice with very few legal consequences. 

Lockdown – the government bans large gatherings, institutes mandatory mask-wearing, restricts the ability for people to go to shops, among other measures.

School Boards

Stay open – school boards keep schools open. The school provides limited restrictions including masks and easy access to hand sanitizers.

Online schooling – the school board shuts down schools and instead provides online schooling alternatives for students.


Go to school – they choose to send their children to go to school in-person.

Pursue online option – they choose to pursue an online option. This may look like anything from accessing classrooms virtually or even homeschooling.

Payoffs and justification

Here, I make a number of major assumptions. Firstly, that the goal of the government is, first and foremost, to reduce the amount of COVID cases that exist. While this is not the case in many countries, I believe that this is accurate in many instances since governments are often blamed for any COVID outbreak that exists. Secondly, that school boards want families to go to school if they are open. This is because often these boards are elected as well and therefore they want to capture the opinions of as many families as well. Lastly, I assume that most families want to lower the risk of COVID, but still want a good education and lowered income inequality overall. While these are not the only assumptions made, these are ones that are common through all of the outcomes. The rest are discussed below in the justifications section.



Payoff (government, school boards, families)




In this scenario, the COVID pandemic spreads widely due to a lack of restrictions. This looks badly on governments and they can be assigned significant blame. As a result, this is an undesirable outcome for them. For school boards, there are likely to be some outbreaks due to the sheer amount of cases, which also reflects badly. However, since families are going to school in-person, there is some political push to keep schools open so this is not the worst outcome for both the government and for school boards. Since families decide to go to school, they lose out since their kids and themselves have the highest risk of getting sick.



In this scenario, the COVID pandemic spreads widely due to a lack of restrictions, but not as much as in A since families are voluntarily staying home. This not only reflects badly on governments and school boards, but since families are staying at home, it suggests that their decisions are not popular either. As a result, this is the worst outcome for both of them. For families, this is not the best outcome since they have to pursue online options instead which may be worse for schooling. On the other hand, they have the significant benefit of children not getting sick.



In this scenario, the COVID pandemic is spreading somewhat widely since there is a lack of restrictions societally, but is not as uncontrollable as in A and B since the school boards have decided to limit the spread by providing the online option. For most families, this is good since there is a lower risk of catching COVID, but there is still significant harm done to lower-income individuals who are met with massive inequality.



If the government enters lockdown, society sees a massive reduction in the amount of COVID cases that exist. This is usually beneficial for their popularity. School boards keep their schools open, but this is not as problematic since the amount of cases societally is lowered. On the other hand, since some schools still see outbreaks, the societal amount of cases is not minimized. Since families are going to school, there is still a risk of COVID, but students get better learning experiences and there is less income inequality.



If the government enters lockdown, society sees a massive reduction in the amount of COVID cases that exist. This is usually beneficial for their popularity. School boards keep their schools open, but this is not as problematic since the amount of cases societally is lowered. On the other hand, families choose not to go to school, which reflects badly on the school board. For families, they reduce the risk of COVID significantly, but children receive worse learning experiences and there is more inequality.



In this scenario, the amount of COVID cases is minimized since both the government and school boards have strict regulations. Schools are closed, which helps to flatten the curve. Families have very small risk of getting COVID, but children receive worse learning experiences and there is more inequality.


Solution to the game

Shown below is the sequential game with all of the payoffs included. 

Here, if the society was opened up, families felt uncomfortable going to school even if school boards decided to keep schools open and decided to stay home instead due to the large amounts of cases. However, if a lockdown was imposed, families would go to school if they were open because they felt like the risk of COVID was minimized enough to do so. 

In this case, school boards tend to take the same decisions as families. This makes sense since school boards are often elected and as a result, follow similar decisions as families. So, if the government stays open, school boards decide to go into online schooling, and if the government enters locking, school boards decided to stay open. 

Finally, the government decides to enter lockdown since this would significantly reduce the number of COVID cases that exist within society as a whole. 


The overall payoff to the game is 60 to the government, 70 to the school board, and 75 to families. This occurs when the government enters lockdown, the school board decides to keep schools open, and families decide to go to school.


Interpretation of the results

We need to keep in mind that different families, school boards, and governments have different situations and priorities. As a result, this is not generalizable everywhere or applicable to everyone. However, I think this result is still significantly valuable. This is because this problem is one that my family, along with many other families around the world, are facing. 

To be honest, this outcome surprised me. I had originally thought that a full lockdown with schools closed would be the outcome chosen. After all, online schooling is the option that our family is currently pursuing. This is starting to make me reconsider what option to take and which governmental policies I support 

Sometimes, a solution derived using game theory is one that is not optimal for any of the players, and in fact, the COVID has been widely compared to the Prisoner’s Dilemma. However, in this scenario, I am not sure if there is one correct answer. Any decision or payoff has severe negative consequences for a portion of the population. 

Hopefully, with the development of new vaccines that will give immunity to the disease, most of these tradeoffs will become clearer. However, until then, we will all have to continue to abide by COVID-19 restrictions and carefully consider what the optimal policy is. 

Works Cited

Arthur, Bruce. “Peel’s Decision to Close Schools Is One Example of Courage in the COVID-19 Battle. If Only the Courageous Had More Power.”, 5 Apr. 2021, 

“Considerations for School Closure .” Centers for Disease Control and Prevention, 

“Education: From Disruption to Recovery.” UNESCO, 7 Apr. 2021, 

Jennifer Couzin-FrankelMar. 10, 2020, et al. “Does Closing Schools Slow the Spread of Coronavirus? Past Outbreaks Provide Clues.” Science, 26 Mar. 2020, 

Kristof, Nicholas. “When Trump Was Right and Many Democrats Wrong.” The New York Times, The New York Times, 19 Nov. 2020, 

Rettner, Rachael. “Should Schools Close for Coronavirus?” LiveScience, Purch, 5 Mar. 2020, 

“What Works to Flatten the Curve and What Science Says on Easing Restrictions | CBC News.” CBCnews, CBC/Radio Canada, 9 May 2020, 


  1. Really interesting stuff Adam, my big question is what exactly do the payoff numbers mean? To that extent, is there hard evidence of what path is the best as a whole in real life?

  2. Hi Adam, I really enjoyed learning about the outcomes and different paths one could take. I like how you used game theory to do this, but what exactly do the pay off rates represent?

  3. Hi Adam. I thoroughly enjoyed reading your Catalyst project! Thank you for taking on the task of answering this difficult question—an approach using game theory is an incredibly interesting approach. I’ve written some feedback below: note that most of the feedback is critical, given that it would be counterproductive to focus on all of the good things.

    Feedback by section:
    Setup of the game
    I agree that a sequential model would fit best for the design of this particular game, as it demonstrates possible options and outcomes in a clear manner. Personally, I was wondering if there was a possibility to expand the number of options that the players have, beyond just “Stay Open” and “Enter Lockdown”. The same feedback applies to schools and how they make decisions. Although it is true that they can either “Stay Open” or pursue “Online Schooling,” many institutions across the world have opted for a hybrid system. For instance, I personally know that many schools in Montreal have reduced capacity systems, where certain grades will go every other day rather than every day. This is impactful because it may alter the payoff matrix: hybrid learning can reduce the negative externality associated with COVID-19, and can still relatively maintain the benefits of in-person education.
    Here are some additional “lingering questions” I have of the setup.
    Where in the world is the game located? Somewhere with high rates of COVID or low?
    Is this in the developing world?
    In terms of the location of the game: how well is the nation doing in terms of vaccination progress?
    CAN these countries decide on full lockdown to begin with? Is it a democracy? Or is it a dictatorship with full autonomy?

    Payoffs and justification
    The biggest concern I had with the payoff matrix was what each numerical value represented. What scale does the payoff matrix operate on. Is an increase from 5 to 10 significant? What about negative externalities? This might stem from a personal lack of how game theory works (although I have some knowledge from taking Macroeconomics), but the scale and the payoff matrix seems to be the most ambiguous part of this section.
    A rational person would make inferences here about what the scale means, but this is difficult given your chosen format of (x,y,z). Not too sure what each numerical value represents.
    By intuition however, the values seem justified. A safe society should have a high score, and an unsafe society should have a low one. To summarize, a legend or scale would be beneficial for clarity.

    Solution to the game
    In your proposed solution to the game, where the payoff matrix is (60, 70, 75), I wonder if entering lockdown would actually be such a sizable benefit for the government. Many areas around the world oppose lockdown, citing unfair restrictions on movement, rights and freedoms. Would this maybe impact how large this payoff amount is?
    I also wonder if 70 is too large for schools as well; after all, they do have to lockdown.

    Interpretation of the results
    The first part of this section is a concession/assumption, stating that different families, school boards, and governments have different problems, and will thus, yield different results. Perhaps this would be of more benefit to the project if you moved it at the top.
    I appreciate the comparison of this payoff matrix to the Prisoner’s Dilemma. After examining the sequential game myself, I couldn’t really pinpoint what the best solution is.

    Perhaps more variance in colour, font type, and font size would help boost the aesthetics and appealability of this project. Currently, it may be difficult for readers to digest the amount of grey text there is on the project page.

  4. Hey Adam, I was really intrigued with your Catalyst project as it really relates to us all during these troubling times. I can personally relate to the stress and foggy moods that have been so prevalent since the start of the pandemic. It’s really interesting how you used game theory to propose a solution and how you had your payoffs and justifications. Overall, really well-done job, however, I was wondering what do the pay-off rates mean. It was bothering me as I didn’t seem to understand it.

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