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Social network-based distancing strategies to flatten the COVID-19 curve in a post-lockdown world


Our class has a clear focus in networks, crowds, and markets. It’s crosslisted in the departments of information science, sociology, and economies. There’s a multi-disciplinary application to the many problems and concepts that we go over. The very first concept that we went over was graphs. In my opinion, it’s one of the most versatile ways to represent data ranging from modeling populations to nuances in classical music and everything in between. This blog post focuses on a research article that uses social network-based distancing strategies to counter the COVID-19 pandemic. I believe it’s quite relevant as a majority of Americans work from home or attend remote learning classes at their respective institutions. It’s been over half a year since this disease has impacted the world. Socially, psychologically, and economically it has caused waves throughout every age group and every part of society. We haven’t seen a pandemic this serious in over a century and it’s imperative for us to be safe. In a world where technology dominates our everyday lives, it’s interesting to see how scientists do research to limit interactions and modeling that using graph theory.


The graph below is a visual representation of two example networks that have the same number of individuals and social interactions. The key differences are the paths taken. The bold lines are the shortest infection path from the infection source to the last infected individual. We hear the phrase flatten the curve very often but having the graph helps understand how important it is to social distance. Similar to the models being done to contain COVID-19 spread at Cornell by professor Peter Frazier, these models try to take into account real world contact networks and model different strategies over time. The researchers propose three different strategies. The first is seek similarity. Individuals choose their contact partners based on similarity of a predetermined individual characteristic such as living in the same neighborhood or classmates. The second is strengthen communities. Individuals consider with whom their contact partners usually interact with and as such an individual should limit interaction with those they aren’t mutually connected with. The third and final is build bubbles through repeated contact. Individuals decide whom they usually interact with and slowly restrict those interactions. The models and graphs that are present in the research paper help explore and visualize these three strategies. The walk away with each one slowing the spread of the virus as compared to no intervention or non-strategic social distancing. From this paper, I understand the importance of having several different test cases in the research that one would do in order to narrow down the most effective ones. In addition, it’s good to see that the concepts that we learn in class are constantly being used in the real world to solve very pressing issues.


Game Theory in Hurricane Support

This semester, I am studying from home in Gulf Coast Florida. About 2 weeks ago, we were hit by Hurricane Sally. The entire week before and after Sally directly passed our area, heavy rain and wind pounded our window day and night. The night the hurricane actually hit, our phones vibrated multiple times throughout the night, with flash flood warnings and tornado warnings. News channels on TV monitored Sally throughout the night, continuously showing how the hurricane is moving on a map of our area. We live on the second floor of an apartment, and I could feel the building slightly shaking from the winds. The wind slashing at our windows was so loud that I was not able to sleep at all that night. Power kept going in and out, and wifi went out the day after the storm passed. Our nearby Walmart suffered a long power outage, which resulted in them getting rid of all their refrigerated goods. Trees were snapped, leaves and branches scattered all over the road, sometimes landing on a house, damaging the roof. The hurricane passed but left many people unable to return home because of the damage to their houses (broken roof, water in the house, trees blocking the door, etc).

After experiencing such a deadly hurricane for the first time in my life, I finally understood how after every natural disaster, there were so many people in need of help. This article examines how natural disaster responses from nonprofit organizations can be made smoother through game theory: It was written after Hurricane Harvey hit in 2017, and used data from Hurricane Katrina for their study. They studied games played by NGOs when dealing with competing to get funding and trying to send appropriate relief items to areas in need. They examined 2 scenarios:

  1. When the NGOs were free from satisfying common minimum and maximum amounts of the relief item demands at points of need (a Nash Equilibrium model);
  2. When the NGOs had to make sure they delivered the minimum needed supplies at each demand point for the victims but did not exceed the maximum amounts set by a higher-level organization.

With scenario 1, NGOs can actually try to choose the easy way of sending out relief items, which could lead to some areas not receiving the needed items. Therefore scenario 2 constraints are needed to guarantee efficient allocation of items to everyone in need. The results of the study showed that it is crucial for NGOs to cooperate and coordinate with each other to yield the best results for everyone (NGOs and victims of natural disasters).

Natural disasters could happen any time anywhere and if game theory can help with the aftermath, it should be studied and used more widely.

Foot Traffic During the Age of COVID 

This research paper provides a mathematical analysis of foot traffic in an academic building in the time of COVID-19. Three assumptions are made: the risk of infection is correlated to exposure rate and time, exposure rate goes down as distance increases, and small exposure to a large group is seen as the same as a large exposure to a small group. The study found that in order to minimize risk, you must minimize exposure time (time spent in passing in hallways, for example). One-way foot traffic increases the time spent in hallways since students must now figure out how to get to their next class while abiding by the walkway direction, which could mean taking a longer route. 

Ever since the implementation of directional walkways during the age of COVID, I had wondered what all went into determining these walkways. This study gave me a little insight into what administrations are thinking about when designing their directional walkways. There is obviously a lot more biological factors that go into the design, but looking solely at paths, it made me think about network traffic. 

In chapter 6 of the course textbook, we learned that transportation networks involved fundamentally game-theoretic reasoning since players aren’t just concerned about choosing a route, they’re also concerned about congestion which can impact their travel time. In chapter 8 of the course textbook, we looked at these traffic networks again but this time added quantities and thought about Nash Equilibrium. We also introduced and dwelled upon Dietrich Braess’s 1968 paradox. These teachings relate to foot traffic in the age of COVID because the designers must view travel times as exposure times and will want to minimize it for all players (pedestrians). An interesting aspect, however, is that the administration has the power to manipulate the player’s choices. They can regulate the number of people occupying the walkways at a time and direct students to use other paths. As more studies like this one are released, it will be interesting to observe the mathematics and game theory behind foot traffic in the age of COVID. 

Using Game Theory to Battle Wild Fires

Wildfires have become all too common in the United States. Being from California myself, I have witnesses wildfires become an anual concern as they consistently cause enormous damage to my neighboring communities. 

This year, California has witnessed especially devastating wildfires. This season alone, almost 4 million acres have been burnt in the state, 96,000 residents have been evacuated, and and 30 lives have been lost with little hope in sight. With only 6% of the current fire outbreak contained, this fight with fires is far from over. It was while reading these devastating statistics in the news this morning that I realized I wanted to investigate the connection between wildfires and networks.

As I started my research, I fell upon a study which peaked my interested with its correlation to a major topic of the course: game theory.  A 2013 study by the University of Waterloo described how different fire agencies interact when an agency is overloaded. The study’s discussion of the competitive nature around the limited fire-battling resources made me want to draw out a payoff matrix representing the dilemma agencies are faced with when fighting fires.

Although the study didn’t include a matrix, it did provide a rationale for potential payoffs which helped me craft my own matrix displayed above. For example, it was explained that a non distressed agency would feel social responsible to help a distressed one. Specifically, the article mentions how “social goodwill” incentivizes the agencies to aid each other, ultimately giving the agency that shares its resources a positive payoff. Of course, this concept wouldn’t apply to a distressed agency which gravely needs to reserve its resources. When the non distressed agency receives resources from the distressed agency, the additional resources have no result on its payoff, as the resources pose no value to a stable agency. On the other hand, the distressed agency is at a major loss as it gave away its much needed resources.  Ultimately, when looking at the payoff matrix based off the study, we observe that both agencies have a dominant strategy. For the distressed agency, no sharing its resources will result in better payouts all around. Alternatively, the non distressed agency has a dominant strategy of sharing its resources and aiding the agency in need. Furthermore, the pure Nash equilibrium sits in the bottom left square, where the best outcome for both agencies occurs when they share resources to the one in need, and reserve their resources when under pressure. In conclusion, game theory helps give us insight on how fire agencies interact in a mutually beneficial manner while under pressure from fires and explains the enormously collaborative nature of the industry .

All in all, I found this application of game theory to be interesting in its application to a real world issue which involves solving problems. In its traditional applications, game theory includes two players going head to head, trying to win to a near malicious extent. However, this application demonstrates how game theory can be present in almost any competition, even when the two ‘players’ have a common goal.



LinkedIn Limits Spread of QAnon Misinformation

This news article talked about LinkedIn’s most recent action in limiting the spread of QAnon group misinformation on its professional network. QAnon supporters promote far-right conspiracy theory, and LinkedIn has been hunting down there misinformative posts at their infancy and removing accounts that were posting them due to a violation of LinkedIn’s professional policy.

It’s been a critical question about how much social media companies should interfere with online free speech. There is a fine line between providing a safe online environment for users by practicing censorship and allowing enough freedom to all users. In this world of digital freedom and low entrance bar to voice an opinion online, it is extremely hard to monitor the spread of a particular group and limit its spread. A community can sprung up overnight by connecting thousands of users together, all from different networks. The formation of an online community is by combining originally separate network groups together, building bridge between them, and leading to the expansion of more connections. LinkedIn’s effort need to be further reinforced with strong measures to be taken to ensure maximum effect on these community networks.

The concept of the spread of misinformation on social media is based on what we learned in Networks. Nodes are interconnected to form different networks, and when people on social media start to reach out to other networks and build bridges between different groups, these separate networks become connected as well and form a mega network. There’s also the concept that if one person has good relationship with two other connected nodes, the other two people will likely form a positive relationship as well, which is how these communities are built on. It’s through the spread of words between connected nodes and likely their mutual connections and eventually extend to different networks. In order for LinkedIn to totally eliminate such group that spreads misinformation online, they need to find the bridges that connect these groups and possibly recognize spam accounts that spread misinformation.

The Global Music Network: Is BTS the Bridge?

Korean pop boy band BTS is known as the K-pop artist to transcend language barriers and become an international sensation overseas. In a March 2020 article by the Wall Street Journal, “Seven Reasons Why South Korea’s BTS Is an American Phenomenon,” the author of the article dubs BTS as an American “success story,” being the first of the K-pop genre to “top the U.S. album chart” and “perform at the Grammys.” BTS has collaborated with several American musicians and is a large contributor to recognition for Korean music in the United States.

In other words, the WSJ article implies that cultural music genres evolved simultaneously, but separately, and BTS and American recognition connected these two industries. If we look at all musicians as a network, then the American and Korean music industries were separate giant components (each consisting of their own artists), and BTS bridged the two, thus creating one giant component. 

However, this relationship does not serve as a bridge according to the network definition because:

1. BTS’s tie to the American music industry is strong.

As established earlier, BTS has collaborated with several American artists and has met them at award shows. Therefore, BTS has strong ties with American musicians. Naturally, BTS also has strong ties to other K-pop artists because they belong to the same genre. Because of the strong triadic closure property, weak ties may form between BTS’s strong ties. This has proven to be true as more Western and Korean artists began to work together. BTS actually serves as a node that is deeply embedded in the network, as opposed to a bridge. 

2. The two industries were already connected through neighbors.

Additionally, even before BTS came to fame, it was common for Korean companies to hire American songwriters to write their music. Instead of direct collaborations, the K-pop artist would be connected to a Korean producer, the Korean producer would be connected to an American company who would be connected to their employee to write music for Korean songs, who was previous connections with other American artists they’ve worked with. Though this is not a direct collaboration between artists, they have still been part of the same giant component.

Though the WSJ gave BTS immense praise for paving the way for other Korean artists, the more accurate way to describe the relationship between these two connected components and BTS’s role in the global music network is that there initially could have been a local bridge between BTS and the American music industry. The tie strengthened, and as a result of the triadic closure property, BTS became a deeply embedded node in the global music network, sharing many neighbors between industries.


Polygons, Segregation, and Nash Equilibrium

While researching ideas for my blog post I came across a website Parable of the Polygon created by Vi Hart and Nicky Case. This website creates an interactable model demonstrating the Thomas Schelling 1971 paper Dynamic Models of Segregation. Schelling’s segregation model essentially states that in a larger system –or game –of housing/neighborly relationships small individual biases can domino effect into a large collect bias (i.e. segregation).

In Parable of the Polygon, this game of neighbor dynamics is represented by squares and triangles that want to have at least a certain percentage of their neighbors to be their own shape. If triangles/squares’ needs are not met (and are thusly unhappy) the website challenges us to relocate each unhappy polygon. At a preference for greater than or equal to 33%, similar neighbors the effect of the unsatisfied individual segregating the community becomes jarringly apparent (see figure 1 and figure 2).

FIG 1: 33% neighbor preference before sorting (unsatisfied people-characterized by shapes with gaping mouths).

FIG 2: 33% neighbor homogeneity after sorting (satisfied, but now the neighborhood is segregated).


Parable of the Polygons allows us to simulate this phenomenon with other percentage values through running simulations.  It turns out that any percentage above 33% consistently yields a dramatically segregated neighborhood. These staggering results seem to mirror the racial politics regarding the long battle for desegregation in the United States. In fact, desegregation is still being fought today. During as recent as 2016 NPR reported on a Missippi school district finally receiving an order to desegregate.

I believe that the forces at work behind Schelling’s segregation model is very similar to the mixed/pure Nash Equilibrium traffic games that we encountered in class. Instead of drivers, we have polygons, and in the place of roads, we have the unoccupied spaces. In other words, in this game, each unhappy polygon is a player that will need to pick a “strategy” (i.e. find new empty space to move to) based on the “payoff” that the new space provides (i.e. payoff = compliance with the percentage condition). Just like our drivers, the polygons will eventually reach a NE (though the NE may likely be segregated).

So–what are some solutions to that may reverse this segregated result? Simply lowering the bias yields no change in the segregated system since technically living with at least 55% similar neighbors does not violate the lowered condition that one must live with at least 22% similar neighbors.

The solution to this problem is to demand diversity. In other words having a range of preferred similar neighbors, rather than a strict value. Thus from my experience using Parable of the Polygon I learned that in a segregated neighborhood easily influenced by individual bias, the solution is to demand diversity.


The Game Theory behind Asking your Crush Out


As a middle schooler I always feared asking my crush out on a date. Maybe it was the fear of getting rejected or the humiliation from my friends and peers that came with rejection. However, I always wondered if it was anything more than that and if asking your crush out was truly always the best option. It wasn’t until learning about game theory that made me question that asking people out might be more complex than I imagined.


Let’s take the example of something similar to those middle school days. Suppose we are looking at the relation between a boy and a girl who are friends, where either individual can either 1) say you have a crush on them or 2) say they do not have a crush on the other. From the following information, we can set up a 2×2 payoff matrix illustrating the interactions between them: 

Girl saying she has a crush


Girl saying she does not have a crush (NC1)
Boy saying he has a crush


Win/Win scenario which  leads to a date:


Boy gets rejected, yet girl is unharmed


Boy saying he does not have a crush


Girl gets rejected, yet boy is unharmed


Mutual feelings towards each other, no one is harmed



If the girl says that she has a crush on the boy, then the boy’s best response would be to say that he also has a crush on her too. Similarly, If the boy says that he has a crush on the girl, then the girl’s best response would be to say that she also has a crush on him. Since these two are mutual best responses, then (C1,C2) is one  pure strategy Nash Equilibrium. However, if the girl says she does not have a crush on him, then the boy’s best response would be to say he does not have a crush on her because the feeling of rejection is worse than having both of you having no feelings towards each other. Similarly, if the boy says he does not have a crush on her, then the girl’s best response would be to say she does not have a crush on him because like said earlier the feeling of rejection is worse than letting him know they are no more than friends. Since these two are mutual best responses, then (NC1,NC2) is another pure Nash Equilibrium strategy. Therefore, there is no dominant strategy in this scenario because C1 (or saying you have a crush) is not always the best response for the boy. For instance, if the girl decides to do NC2 (say she does not have a crush), then the best strategy for the boy is NC1 and not C1, so there is no dominant strategy.

From this, we can conclude that game theory is not a valid approach to understanding what one should do if debating to ask out a crush. Further, this shows us that there are so many factors that contribute to individuals’ opinions and choices. So, in the future you should most likely shoot your shot because you miss every shot you do not take.

Canadian Snowbirds: Who’s Playing What Game?

An article published by CBC News on September 30th, Why some snowbirds are still heading south this winter despite COVID-19 and a closed land border, starts by centering on the decision by one Canadian snowbird to go on her annual trip to Florida this winter. For context, a different CBC News article states that approximately 350,000 Canadians travel south of the border every year. Obviously this common extended vacation mostly enjoyed by seniors who’re avoiding the discomfort and dangers of winter is being interrupted by Covid-19. Snowbirds have to consider the benefits and risks of staying in a country with lower rates of infection or traveling to another country without the hazards of winter. In addition to Covid infection and winter risks, snowbirds have to consider their mode of transportation; many snowbirds habitually travel by car, but this may not be possible. The US-Canada land border closed to non-essential travel in late March and the closure has been extended until at least late October, although it is suspected the closure will be extended again. Entering the US by air travel is still allowed at this point, but does not serve snowbirds well. The benefits of driving down include having a car at their winter homes and also being able to transport more household items. These are both concerns cited by the snowbird in the CBC article, however she states that she plans on going to Florida even if she must fly.

This article raised many questions about how snowbirds will make their decisions to travel this winter. Referring to game theory, snowbirds could be entrenched in different games with complex payoffs. For example, snowbirds could be a player in a game with the American communities set to receive them. The snowbirds’ options would be (A) travel or (B) not travel, and the American communities’ options would be (A) accept the foreigners or (B) close community to foreigners. At this point it is unclear how many Canadian snowbirds will make the trip down south. Conversely, it seems that most American communities (namely in Florida, California and Arizona) will not hesitate to accept the repeated business of snowbirds. Focusing on the snowbirds as the article does, I struggled to conceptualize their complicated, nuanced payoffs in all four game-related outcomes. After studying a number of keystone games, like the hawk-dove game and the battle of the sexes, I was surprised by how when I considered my own game, each snowbird’s payoffs felt entirely unique. Some snowbirds can’t afford the new costs of traveling, nor the increased insurance rates. Others, like the one in this article, don’t have winterized homes within which to stay if they choose not to travel. Overall, the Canadian snowbirds can be viewed as players engaged in games with local organizations or even federal governments (i.e. Canadian/American travel restrictions), but the payoffs can be trickier to weigh than I once imagined.

Hate Networks on Social Media Platforms

After I graduated from high school, I tried briefly to remain up to date on the various goings-on in the lives of the people I had spent so much time with during my formative years. Facebook was quite popular as a means of publishing details about one’s life and communicating with other people in my hometown, so it seemed like a natural way to stay connected with my friends and acquaintances as we went our separate ways in life. As time went on, it turned out that social networks like Facebook were having an unexpected effect on some of the people I grew up with. The closer I examined some of the posts that a select few of my peers liked and shared, the more apparent it became to me that their personal political views were being slowly but surely pushed in a more hateful direction than any of them had displayed while we were in school together. One only had to click a few links in the right order when investigating one of the posts in question to get into some truly racist and hateful groups and pages. This was alarming to me, but aside from reporting the groups when I stumbled upon them, there was not much that I as an individual could do. This, among other things, contributed to my eventual decision to delete my Facebook account and stop communicating with and thinking about the people whose “personal Overton windows” had been pushed so far in such a hateful direction.

A few months ago, some website algorithm recommended an article called “Strategies for combating online hate”. This piqued my interest, and I read it immediately. The topics it addressed seemed like a perfect fit for a blog post of this nature.


Hate Networks

The article that was recommended to me is an overview of a study that was published in the journal Nature, entitled “Hidden resilience and adaptive dynamics of the global online hate ecology”. The researchers created a model of the way that various “hate clusters” on social media are connected, with “clusters” being defined as “online pages or groups that organized individuals who shared similar views, interests or declared purposes, into communities”. To transition from a list to a network of clusters, researchers considered two clusters to have a connection if each cluster contained a hyperlink to the other cluster. This allowed the researchers to observe network behavior on a larger scale than a simulation of a large number of individual users would have allowed for.

During the course of their research, it was found that hate group clusters are “highly resilient” to various ways of dealing with them. Because clusters are linked not only through hyperlinks, but through users who are members of multiple clusters, banning a given group or page had very little effect on the interconnectedness or growth of a given hate cluster. Instead of dispersing, banning a page or group of users “aggravates online hate ecosystems and promotes the creation of clusters that are not detectable by platform policing (which the authors call ‘dark pools’), where hate content can thrive unchecked.”


New Strategies

The authors of the study present several potential new methods of dealing with hate clusters:

  1. The first strategy suggests that rather than targeting the largest and most visible clusters, a social network should focus on removing the users within smaller, less well-connected clusters. This would allow social networks to avoid the outrage that would come with the removal of a large, well-connected, visible hate cluster while still being able to prevent the rise of new clusters of that type (small clusters can become large ones if they become popular enough). Reddit in particular seems to be experimenting with this strategy by banning smaller subreddits with content they find objectionable. One example of such a recently banned subreddit is /r/ConsumeProduct, which was originally intended to criticize what was seen by its members as excesses in capitalism and consumerism, but had at some point shifted its focus to antisemitic dog-whistles and quotes from Ted Kaczynski’s manifesto (he is better known as the Unabomber).
  2. The second strategy suggests selecting users in clusters at random and banning them in an attempt to weaken the overall connections between various clusters. The effectiveness of this method depends on the topology of the cluster network: a more tightly-knit community might notice users being banned and also not be affected as much as a more loosely-knit community. In addition, a loosely-knit community might be able to be isolated eventually more easily through the random banning approach and then banned entirely once the social network deems it isolated enough.

There are two other strategies that were recommended in the study, but they are less relevant to the content of this class.



If the data supports the efficacy of the strategies proposed by the study, then I they might warrant further testing on actual hate networks rather than on mathematical models. I worry that banning users without offering some alternative to participating in a hate network might cause them to become socially isolated and seek out other extremist groups on other platforms, in which case we’re back to square one. I doubt that social networks will be forthcoming with the methods that they are using, so it also seems unlikely that I’ll be able to associate any of these proposed strategies with any improvement in the beliefs of my former classmates. I hope something works eventually.


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