Welcome to the course blog for MS&E 135 Networks at Stanford University. This course explores how diverse social, economic, and technological systems are built up from connections, and how the study of networks can help us understand these systems.

During the spring quarter of 2016, enrolled undergraduate students will be writing regular posts  on varied subject matters and current events related to the course. Topics include: networked markets, social networks, information networks, the aggregate behavior of crowds, information diffusion, the implications of popular concepts such as “six degrees of separation” and the “friendship paradox.”

The blog is visible to the public, however only students and course staff are able to post and comment. Students should refer to the course blog guide for more information.


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Fighting Crime with the Prisoners’ Dilemma (At Least on TV)

In this clip from the CBS Show Numb3rs, in which a mathematician (Charlie) helps his FBI agent brother (Don) fight crime using his number theory-driven insights, we see Charlie create a prisoners’ dilemma situation to get one of the suspects to talk. Although the show is entertaining and they often reference real mathematical theorems and properties, some mathematicians who have tried many of Charlie’s approaches have found them to not be applicable after all. In this spirit of checking Charlie’s work, I decided to take a clip from the show in which Charlie references game theory (of which there are several) and see if what he says holds water.

First, in his explanation to his brother about what game theory is, he says game theory is the process by which you try to achieve “optimal outcome” from a complex situation – that part sounds all right. Then Charlie provides him with an example: 2 prisoners and how much time they would each serve if they talk or don’t talk and if the other prisoner talks or doesn’t talk. I’ve written up the game set-up below and included an identification of dominant strategies, etc. according to what we’ve learned in class. Looks like Charlie’s example is a good one. Moving forward…


Don presents the case: three men, F, G, and W, have stolen a vehicle filled with civilians that must be found as soon as possible. As they discuss strategy, Don shares the go-to move of keeping the suspects isolated from one another while simultaneously trying to pit them against one another. As we learned, the assumptions behind a game are as follows: (1) payoff summarizes everything a player cares about (2) each player knows everything about the structure of the game: who players are, strategies available to all, payoffs for each player/strategy (3) every player is rational: wants to maximize payoff and succeeds in doing so. According to these assumptions, Don’s own prisoner’s dilemma met all the assumptions of a coordination game – except for the last part of the second assumption: because they were being kept separate, the men did not know about payoffs for each player, they only knew their own. Charlie suggested bringing them together, which rectified this situation. He also looked at a collection of factors such as existing criminal record and connections to family “on the outside” to determine what each man was risking by refusing to act on his dominant strategy (meaning by still choosing to not talk). This way, everyone knew how much was at stake for their accomplices and could consider how that would affect their strategy.

By taking Charlie’s advice, Don changed the dynamic in the room, among the men, and between himself and the men. The following illustration shows the impact of Don asserting himself into the men’s network as the only node connected to all 3 nodes. G had been the center of the chain since he was the ringleader, but now Don boasts the most powerful position because he is connected to all 3 other nodes and could get what he wants from any of them.


In this particular clip, it looks like Charlie’s theory actual worked out flawlessly. Although the game that Charlie proposed for these suspects was viable, the game assumes that every player was rational, which is not always the case with real-live humans. The assumptions behind a game also include that the payoff (or in this case, risk assessment) summarizes everything a player cares about. Since the men’s risk assessments were created by Charlie through the use of factors he anticipated held value for the men, they were automatically a “best guess” because they were not made with complete certainty that these processes summarized everything that was important to these men and impacted their going to prison. Despite these shortcomings however, the idea behind the Charlie’s game theory-inspired strategy holds true: you can influence people better if they see firsthand what they’re up against and a rational actor will adopt their optimal strategy to secure themselves a much greater likelihood of a favorable (or comparatively favorable) outcome.

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“The World is so big, I want to have a look”

Freedom of Speech on Chinese Internet

As a Chinese student studying in the US, I can feel my world expand and shrink every time I cross the borders of these two countries. In America, I am free to post personal updates on Facebook or send a Snapchat of my meal to a friend studying abroad in Europe. I have a network of classmates, friends, family members, and professional connections across all social media platforms. I feel free to be myself and express my own observations, whether they are regarding my dinner at a new restaurant, my view of a historical movement, or my beliefs on the coming up presidential race.

It wasn’t until every time I return home in Shanghai did I realize that I had taken all of my internet rights in the US for granted. In China, my main social media networks, including Facebook, Instagram, Snapchat, Youtube are all blocked. Although if anyone tries hard to “jump over the firewall” by purchasing a VPN, anyone can still visit these websites. But the bigger concern in China is the freedom of speech. Over the course of this quarter with MS&E 135, I have always wondered how network systems, especially on the internet, is different in countries that enforce internet censorship, especially in China. Recently, Quartz’s news article on the popular memes in China caught my eyes.

“The World is so big, I want to have a look”

Above is one of the most popular memes of this past year. It is a quote from a Chinese middle school teacher, Gu Shaoqiang, from central China’s Hunan province as she resigned her job in 2015. This quote became viral on the internet— mostly from Chinese people who are also tired from their jobs. But to me, I believe citizens have been spreading this quote as a message against the Chinese internet censorship. They know that the world is much more complicated and stories can potentially be much different from the national news that display on Chinese news and TVs. There is a longing for freedom of speech.

Such a limit in freedom of speech also limits people’s self-expressions on the web. For instance, if anyone posts about an anti-Chinese view or a quote on Chinese chatting platform WeChat or Twitter Weibo, these posts usually get erased within five minutes. No one wants to mess with that, and as a result, cascading effects take place and views on Chinese social media become more conformed and less “extreme.” People who are anti-internet censorship are blamed as having “Cold War mentality” or hatred towards the country. For example, as Chinese journalist was accused of “arrogance” and “prejudice” for mentioning the lack of human rights in China during a press conference in Ottawa. It is ironic that the Chinese government also uses exactly the same medium— the media— to counteract and oppose those who are “rebellious” against freedom of speech on the internet, by spreading these negative perspectives and ideas of human rights activists. After all, our freedom and rights dictate our expressions, which in turn shape who we are and who we become.

For reference:


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Game Theory Analysis of Penalty Shootouts

Game Theory has been a prominent topic throughout the course and I chose this article because it uses them to analyze one of my passions, soccer.  In this weekend’s Champions League final between Real Madrid and Atletico Madrid, the game was a draw after regulation and came down to a penalty shootout.  In a shootout, players alternate taking one-on-one shots against the goalie.  Due to the short distance between the two players, (12 yards) “guessing” where the ball will be kicked is vital for the goalie.  Game Theory attempts to predict someone’s optimal decision and can be used to model penalty kicks.

Although it is a complex coordination game, I modeled it using four simple choices of where to kick/defend:Screen Shot 2016-06-02 at 3.45.20 PM.pngAs you can see, the only combinations for the goalie to win is choosing the same location as the kicker.  This simple graphic shows that if a penalty kicker and goalie were to make their decision randomly (with each option having a probability of .25), the likelihood of a goal is 12/16, which equates to 75%.  Interestingly enough, in professional soccer, the percentage of penalty kicks made is 73%.  So is it truly a guessing game?

Ignacio Estefanell, the author of the article, believes that both teams chose their kick locations prior to the game and had strategies in place.  All five Real Madrid kickers shot to the keeper’s left, and all four Atletico kickers shot to the keeper’s right.  For as long as soccer is played, economists will attempt to figure out the tendencies of a team but, at the end of the day, there’s always a level of unpredictability in human choice.

Article Link:

Analytics and Agony meet in Champions League Penalty Shootout

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Potential for Zika Outbreak

Zika is now in the United States. Sort of. There has been a birth of a baby in the United States with microcephaly (born with a smaller head and underdeveloped brain) due to the virus, but the virus was contracted in the Honduras.

This article highlights that baby’s poor prognosis and uses the circumstance as an example and reminder of how not to contract Zika.

This article relates to what we discussed in class about biological epidemics and the SIR, or SEIR, or SIS epidemic models. It is unclear what type of model would be best suited for Zika because, as this source articulates, there is a lot we are uncertain of. The probability of having a baby with microcephaly by a women who contracted Zika during her pregnancy is about 1 in 13. Despite this specific population and not crazily frightening probability, the branching process seems pretty straightforward. However, we don’t know what the long term effects of Zika are, meaning that out of those 13  infected women, there is a possibility of other abnormalities if their exposed children are infected as well. The branching process of Zika is probably more complex because the uncertainty of being exposed and or infected or even susceptible or removed is uncertain.

Moreover, will Zika become contractable in the United States by this mother and child? Hopefully not, as its transmission is mainly through mosquitos and sexual contact…but again, there is a lot we do not understand about the spread and and effect of Zika. The CDC recommends that women who are pregnant or who are looking to become pregnant do not travel to Latin America or the Caribbean and to also avoid mosquito bites in those areas. Men can also contract and spread the virus, so using condoms if your partner has traveled to those areas is recommended as well.

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Game theory suggests memory and cooperation evolved

“A new study by Joshua Plotkin, a professor in the Department of Biology in the School of Arts & Sciences, and Alexander Stewart, a former postdoctoral researcher at Penn who is now at University College London,” suggests that enhanced long term memory has a close association with cooperative tendencies in group/sharing environments.

Joshua Plotkin

In their study, they found that “the capacity for longer memories promotes the emergence of cooperation. They also find, perhaps intuitively, that cooperative strategies are more likely to evolve in smaller groups rather than larger ones.” This is an extremely interesting discovery to ponder because although they found that enhanced long term memory indicates group cooperation, they also found that this phenomenon is more common in smaller groups rather than larger groups. Why though?

Personally, I believe that no matter what concept is being evaluated, any tendency will be more apparent in a smaller group because there are less people to evaluate and less major errors to encounter. When looking at a larger group, the large amount of data allows for an increase in inconsistent findings. This idea sits closely with the idea that the less people there are, the less chance there’s that one person who will screw everything up.

“Our analysis sheds light on the circumstances that govern behavior in social situations,” says Plotkin. “We see that longer memories allow for a wider range of behaviors that are cooperative, to the mutual benefit of all the individuals in a given group.”

The actual study itself employed the idea of the renowned “public-goods game” in which an individual decides how much of a personal resource to share with those around them. This is very similar to the $1.00 game that we have explored in class. Although each person could come out with no money, this experiment focuses solely on the concept of actually sharing that wealth rather than scheming for a way to come out with more money than the other person.

“Next for Stewart and Plotkin is to test whether the relationships between memory, group size, and cooperation seen in their analyses hold up in an experimental game with human players.” I think that this quote is very representative of our culture as a whole in that everybody is constantly looking for a way to better our understanding of human nature and technological advances as a whole.




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Reddit Hivemind


Reddit doesn’t get its hivemind reputation for nothing. It is very well known that information cascades or “herding” is super prevalent but until recently not too many studies have been done and reddit hasn’t released their own internal data either. But first, for those that don’t know the website too well,  reddit.com is a website where users can either up vote or down vote user posted content and threads. Reddit then uses an algorithm so that visitors to the site will see the most upvoted and “hot” topics on the front page while the most disliked by the reddit community are relegated to the dark corners of web space.

But enough about the boring mechanics of Reddit. What is truly interesting is that a group of researchers have released an extensive study on Reddit’s voting system. And what does it prove? Turns out people are no better than sheep. When things are upvoted, users are also more likely to upvote. Especially when Louis C.K, Neil deGrasse Tyson, or Riot Game’s dumb decisions on their massive multiplayer game League of Legends is involved. The most fascinating part of the study is that when new threads were given a false positive vote, it generated an incredible snowball effect of 32%. Meanwhile if a brand new reddit thread was given an immediate false negative vote, the results were not as apparent as an information cascade was less likely to occur. But this makes sense! As stated in a recent USC study positive emotions are more contagious than negative ones. As a motto to live by, you can never trust the taste of other people’s dislike.

Another interesting aspect is voter manipulation of Reddit’s algorithm. Companies have started to realize that if they post content on reddit and pay people to just upvote continuously then more and more people can enjoy that great 40 second ad within a 1 minute video. While reddit says they have weeded out most of the biggest perpetrators of this practice, there is a way around it which is not as widely known. Since the first few votes are so incredibly important to creating a snowball effect, there is a way to remain somewhat undetected when upvoting one’s own content: use the search tool. If one searches for your thread through keywords that are relevant to many other threads and use the filters to find one’s specific thread then voila: voter manipulation. Although one can’t do this gather a massive amount of upvotes, it does allow threads an edge over the competition, especially as those first few votes matter so much in creating that snowball effect.


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Stock Market Herding


A combination of low oil prices and turmoil in the China market was believed to have led to the drop you see below in January 2016 of the S&P 500. But were these reasons legit?

2016 drop spy

As the article points out, there may have been evidence of a mild slowdown in China’s economic growth, but nothing near as catastrophic as the drop in the market suggested. Similarly, a decrease in oil prices is generally anticipated to benefit oil consuming countries such as the US by increasing consumer spending and boosting the economy. Instead, headlines claimed that low oil prices lead to a decrease in stock prices. Did these factors really warrant a 10% drop in the market? It seems as though the answer is ‘no’ because just two months later, the market had returned to its original level. So what could be the reason for such a big drop? Herding. Investors are heavily influenced by each other and act upon sudden movements in the market. The general assumption is that if a stock price is moving sharply and I don’t know why, someone knows something that I don’t. Therefore, as an investor, I tend to follow the trend even though I might not know the underlying reason for the selloff. Information cascades happen all the time in the stock market and often lead to overcorrections such as the one in January of this year. Once investors begin to look into the underlying reasons after the fact, they realize the news wasn’t as big a deal as the price change suggested and stock prices recover as they did in March/April.

So what’s the lesson here? Don’t trust anyone.

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Pro Golf, the Stock Market, and Herding

So I am a pretty awful golfer. I spend most of my time on the course, or rather off the course in the sand and fishing golfballs out of the water hazards, so naturally I do not hit many birdies or pars. However, pro golfers get paid to sink pars and birdies consistently. They don’t get paid for playing poorly, and so they only take risky shots when they are in a good position to do so. In a recent Moneyweb article, Cass R. Sunstein brought to light an interesting fact about pro golfers: when faced with a putt of equal distance and degree of difficulty, pro golfers sink the putt with a better percentage when the putt is for par rather than for birdie. This happens because pro golfers are loss-averse. They prefer to lay the ball up closer to the hole rather than risk missing the birdie putt, having the bao-golf-tips-facebookll roll far from the hole, and then ending up with a bogey.

Sunstein made a clever connection between the volatility of the stock market and this behavior among pro golfers. He exclaims that a loss-averse participant in the stock market behaves a lot like a pro golfer in circumstances when market prices start dropping. These loss-averse investors will remove some of their holdings in order to limit their losses in the short run (like a golfer limiting their strokes on a given hole), but over time, these decisions to pull money out of investments hurt, as the small losses add up.

This behavior can spark stock market panics, like the one that occurred in February this year. Many investors start dropping stocks based on the behavior of other investors (by receiving “sell” signals via communication) even when metrics and the probability of gain are in the investor’s favor, resulting in the continued loss of value for a single stock or the stock market as a whole. Massive stock sell offs are an example of negative informational effects in cascading behavior. By following the information of others and becoming part of a cascade rather than following reason, the sellers often lose in the long-run, as more savvy investors, those who do not fall into the trap of a cascade, start buying the stocks based on fact and the stock prices go up. These informed investors are important for balancing out the market and preventing the cascade from causing a complete market failure.

We should not just take away from this the lesson that we need to just recognize informational cascades and rely solely on our own information. Rather, we, as future leaders, especially aspiring political leaders and economic experts, need to recognize the power that credentials have over the masses, and use this to not spread extreme emotions among the public, as heightened fear or excitement in a financial market can lead to crashes. President Franklin D. Roosevelt famously coined the phrase, “We have nothing to fear but fear itself”, recognizing that public confidence in the market was essential to avoiding detrimental informational cascades. However, overconfidence can lead to market bubbles, which can be equally harmful to the economy– for example, the housing bubble that burst in 2008.




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Information Cascades Against Clusters

Looking at it from a distance, information cascades seem fairly simple. If the two people going before you picked a ball out of a bucket and declared that both the balls were blue, you go and state that the bucket is “majority blue” even if you pick a red ball. It’s simple right? Although we have used cascades for primitive examples for the scope of our class, information cascades and the herding effects that come with it impact our world drastically.



In 2011, an Economist article aimed to tackle the Arab Spring through herding. The author of the article quoted a paper written by Oregon Economics Professors Chris Ellis and John Fender, where they described revolutions and civil unrest through information cascades. They defined these cascades as a phenomena that forced people to “make decisions on the basis of their observations of other peoples’ actions” and observing signals through their behaviors. They believed that workers decided whether to rebel or not by observing their counterparts actions and though of other workers rebellions as a sign of the regime’s weakness. If enough of them organized and rebelled, then a good shot was born for the regime to be overthrown.

The Economist used this bit to explain the Arab spring, where information cascades both within countries and between countries, created an avalanche effect that took the whole world even the protestors themselves by surprise. Events like these are actual testimonies to just how effective and sudden information cascades can take over.

But we know that virtually every country on Earth has protestors and citizens that want to topple the government or establish the rule of a new leader or new ideology. So why can’t all these movements take off and use the avalanche effect created by cascades? Clusters.

Clusters are closely knitted communities of people that typically share the same beliefs about political issues. And each informational cascade has an innate threshold. A threshold is a magical ratio between the nodes in a person’s network that believe in a given ideology and the total number of nodes in that persons network. For an information cascade to influence an individual this threshold has to be surpassed and significant majority of the nodes in a person’s network should believe in that ideology. However clusters characteristically force people to share a tight group of neighbors and have densities that prevent these cascades from claiming one of their members. And the natural by-product of this clash between cascades and clusters is polarization.

Several posts in this blog have explained the polarization between conservatives and liberals in the US growing due to these clusters; and they are right. However, this phenomenon represents a more global trend.

https://www.washingtonpost.com/news/monkey-cage/wp/2013/10/10/maps-of-global-polarization/ The Washington Post published an article that described polarization in the world and in between the different cultures and governments of the world.


We don’t need to go into the underlying details of the map, but it basically depicts different ideologies with different colors. And the vast difference between the colors of our world is striking. This is the result of a battle between information cascades that aim to create global revolutions and national clusters that want to protect their own ways of life. It will be exciting to see how this will pay out.

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Polarization in US Politics

In mid 2014, the Pew Research Center published an article titled, “7 things to know about polarization in America”. The findings were the following: First, over the past twenty years, the percentage of Americans who express consistent ideological views has doubled. Second, partisan animosity has increased. Third, people surround themselves mostly by people of the same political views. Fourth, communities from the left and right differ drastically in terms of religious and ethnic affiliations. Fifth, there are fewer moderates. Sixth, the most ideologically extreme people get most involved in US politics. Seventh, compromise means getting more instituted from one’s own ideology.

Unsurprisingly, the 2016 election has so far exhibited an affinity for extremes. Yes- primaries have always been less moderate than the general election, yet presidential candidates have not before called to ban all Muslims from entering the country…. While many sociologists have blamed factors such as the two party system and the media for the phenomenon of polarization, Jon Evans from TechCrunch has offered us a new way to think about this polarization: power laws.

As we learned in Chapter 18 of the class, empirical studies on web pages have shown popularity follows a power law due to correlated decision making across our populations. We like to copy the decisions of others because doing so may be the rational thing to do. This same logic can apply to political choice, which is clearly correlated across populations.

So why has polarization increased then? In an age of social interconnectedness, social networks have facilitated the display of other peoples’ beliefs and ideas. As the article emphasizes, Facebook has greatly contributed to this divide. Since people of the same regions and political parties tend to be friends, “conservatives see conservative stories, and liberals see liberal ones […] liking opinions that tell us we’re right instead of engaging with viewpoints that make us question our assumptions”. In so, “filter bubbles” are created and precipitate extremes.

Whether this is good or bad is still up for debate. However, an awareness of the perpetuation of power laws associated with social networks will hopefully give us greater insight into how to deal with the changing face of US politics (and other spheres) in the upcoming years.

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