Wolfram Alpha and Facebook
http://www.wolframalpha.com/facebook/
Until this past week, I primarily used the website Wolfram Alpha as a powerful online calculator to help me solve difficult integrals or large systems of equations. However, one of my friends recently introduced me to another feature of this self-described “computational knowledge engine.” Wolfram Alpha and Facebook have partnered up to provide Facebook users with the opportunity to analytically view their behavior on the social media website. In a matter of a few seconds, Wolfram Alpha generates a lengthy list of statistics, facts, and figures to fully characterize one’s existence on Facebook.This tool provides a unique opportunity to Facebook users. It’s nearly impossible to keep track of all of your interactions with Facebook. You may frequently chat your friends, write on their walls, upload a photo, and tag them in your statuses throughout the day. This task becomes even harder when you take into account that Facebook can be reached by mobile devices in addition to standard computers. In order to fully characterize your existence on Facebook, you’d not only have to keep tabs on everything I just mentioned, but also keep track of when your friends interact with you. You could imagine how daunting this task would become if you have thousands of friends with tens of them liking your status each time you update it. Fortunately for us, Wolfram Alpha is able to quickly sort through our entire Facebook history and do exactly that. It keeps track of which friends you interact with and which ways you interact with them. It also provides you feedback with specific statistical information like your most frequently used words in all of your posts.
Perhaps the most interesting element in the report generated by Wolfram Alpha is the friend network section of the report. In this section, Wolfram Alpha creates an interactive graph of all of your friends and how they are connected to one another. If two of your friends are Faceboook friends with one another, their nodes are connected by an edge. Unfortunately, this tool doesn’t have any indication of strong relationships or weak relationships. What it does offer is the ability to filter the nodes. You can see the differences between the networks of your friends who are older than you and younger than you, and you can also filter by gender.
Wolfram Alpha’s second interesting plot is a “color-coded friend network.” Among others, this graph identifies social insiders, and social connectors. These relate to some of the concepts discussed in Chapter 3 of the text, specifically relationship strength of nodes and partitioning of the graph. As can be derived from Figures 1 and 2, the social insiders tend to have many connections, most of whom are likely to be strong, to a large number of a specific cluster of friends. These social insiders can be found primarily in the center of their respective cluster. Social connectors on the other hand can be found towards the edges of the clusters and tend to have more connections to multiple clusters. The graph in Figure 1 was partitioned into the following categories: those who go to Cornell, those who went to my high school, and “other”. It can be seen that the natural partitions created by Wolfram Alpha rarely have the social insiders at the border and that the social connectors are more likely to be on or near the borders. This is a great real-life example to help people understand social networks and how social circles are related to one another.
Prisoner’s Dilemma at the Dinner Table
We have all gone out to dinner at a nice restaurant with friends, but most of us have never had to worry about getting “betrayed” by our friends and getting a dish of chicken’s foot soup instead of what we ordered. This situation, however, is fairly common while participating in an interesting new twist on going out to dinner, appropriately called “The Betrayer’s Banquet.” This interesting twist on going out for dinner creates a unique experience melding both a theatrical dinner with the game theory model commonly referred to as “The Prisoner’s Dilemma.”
As described by the author’s experience, all the participants of “The Betrayer’s Banquet” gather at a secret location decided the host and they are all dealt a playing card. This card decides each participant’s starting position on the dinner table, where the top of the table is served fine cuisine and the further from the top we go, the less appetizing to food becomes. However, each participant had the ability to work their way up towards the top of the table by playing a round of the prisoner’s dilemma. When pairs of participants sitting opposite each other played the game, they each got a token which had a side representing cooperation and another which represented betrayal. If both players cooperated, then they were rewarded by moving up 5 seats, while if they both betrayed then they both moved down 5 seats. However, if one betrayed while the other cooperated, the betrayer would be rewarded by moving up 10 seats while the person who cooperated would move down 10 seats. This dinner setup is exactly like the examples of the Prisoner’s Dilemma that we studied in class and from chapter 6 in the textbook, while learning about game theory. Based on what we learned, the Nash equilibrium for both of the participants in the game, if they didn’t know what the other would choose, would be to pick betray, as this would be the best choice. This, however, may not work in this particular game since although both participants are unaware of each other’s current choices, they may be aware of each other’s previous choices. This may lead participants, like the author, to match the opposing party’s previous behavior. If a person has a track record for always cooperating than it may be beneficial to cooperate with the same partner multiple times and make it all the way to the front. However, if your current partner has a track record for betraying often, then it may be in your best interest to betray your partner as well. Since we are not oblivious to our partner’s past decisions, the optimal strategy for the prisoner’s dilemma does not remain the same. Overall, it is very interesting to see how “The Prisoner’s Dilemma” has been adapted to help create an innovative an interesting dinner experience.
Source:http://www.newscientist.com/article/dn24276-how-the-prisoners-dilemma-changes-dinersetiquette.html#.Uk43X4Ym2KE
The Importance of Networking
Why does networking still take place in an age where electronic advertising and social media are taking over lives by the second? The business insider claims that networking is one of the most valuable uses in terms of returns. He states that “most of these social networking events provide a laid back atmosphere to chat with similar people, and these informal chats often lead to many opportunities and potential ways [to] work together.”
Networking can help spread the name of your business. This statement can be supported by the theory of strong and weak ties in Chapter 3 of Networks, Crowds, and Markets. Two individuals can have a strong tie or a weak tie. A strong is one in which they can be considered “good friends,” while a weak tie can be considered “acquaintances.” It has been shown that news is spread via weak ties, which are formed in high volumes during networking events, because a group of friends, interconnected with strong ties share much of the same knowledge due to their similar interactions with their friend groups. A weak tie would allow the spread of information between acquaintances who are both part of their own close friend group. These weak ties may also serves as bridges between two groups who were originally not linked. The bridge functions as a pathway for information, knowledge, etc to travel through.
However, electronic advertising and social media can also spread information and serve as bridges. Considering the two services serve the same goals, the biggest challenge of the electronic age is the difficulty in predicting human patterns. For example, when using Facebook as a connection, two people who have been using Facebook and have not added each other as friends are most likely not friends or have a particular reason why they are not friends. The advantage that these networking events is their ability to introduce weak ties, which are important for expanding a network.
Networking “events are all about mutual benefits… There will be times when you may need help or advice.” For example if you had more ties to the person who you would like to business with, the person would be more trusting of you due to the mutual friends or acquaintances and there will be a higher probability that he will help you. “Your net worth is only as good as your network.” The benefits that a network may provide cannot be substituted by electronic advertising and social media, but only enhanced.
http://www.businessinsider.com/the-importance-of-networking-2011-5
Braess Paradox and Basketball
When presented with a range of options, it is generally assumed that rational people are able to organize those options by value in order to make a best choice. This is a fundamental assumption behind what economists refer to as selfinterested behavior. When choosing who to pass to during a basketball game or routes on the drive home, people will select the best options from a range of alternatives because a selfinterested person will make selections which maximize their utility. However, what if everyone else makes the same choice?
Assuming some depreciation of an option due to overselection, selfinterested behavior can lead to being worseoff in the presence of better options. When 42nd street in New York City a major artery of the metropolitan traffic network was shut down for Earth Day citizens feared that closure of the almost always congested but most direct roadway through the city would lead to even more congestion. To the surprise of many New Yorkers traffic flowed smoothly. Without the more direct 42nd street as an alternative,self interested drivers chose other routes, distributing vehicles throughout the NYC traffic network instead of all piling onto the single most direct option (Kolata, New York Times, 25 December 1990). Dietrich Braess, a german mathematician, first recognized this phenomenon, known as Braess Paradox, where the relative utility to a best option declines as self interested people pile on.
Braess observed this outcome by paying attention to roadway construction, but the paradox of worseoutcomes (i.e., increased travel time) corresponding to improved options (i.e., newfaster roadways) extends beyond traffic networks. Consider the passing behavior of a basketball team as similar to the flow of vehicles within a traffic network. Conceivably by removing the best players (passing options) from a team might improve the team’s performance. This basketball analogy is playfully regarded as the Ewing Theory,suggesting that Patrick Ewing’s teams for some reason played better when the Hall of Fame player was either injured or away (Simons, 2001). Skinner, 2009 draws out this connection between the team sport and traffic planning further in the referenced blog post.
Network science principles can be applied to understand a variety of situations, it is a matter of framing the problem and network relationships in order to better understand the underlying dynamics. Braess paradox is among the more well known outcomes to selfinterested behavior on a traffic network. What other domains could these concepts be applied to better understand the flow of people, cars, energy, information or anything else?
REFERENCES
Kolata, G., “What if they closed 42nd Street and nobody noticed?” New York Times, 25 December 1990.
Accessed electronically on 3 October 2013 from online source
http://www.nytimes.com/1990/12/25/health/whatiftheyclosed42dstreetandnobodynoticed.html
Simons, B., “Ewing Theory 101,” ESPN Page 2, 9 May 2001. Accessed electronically on 3 October 2013
from online source http://sports.espn.go.com/espn/page2/story?page=simmons/010509a.
Skinner, B., “Braess’s Paradox and The Ewing Theory,” Post on the blog “Gravity and Levity,” 28 May 2009.
Accessed electronically on 3 October 2013 from online source
http://gravityandlevity.wordpress.com/2009/05/28/braesssparadoxandtheewingtheory/
Intra-guild Networks and Communities in Massive Multilayer Online Games
When discussing networks of relationships, we generally think of communities built upon geological proximity i.e. our interactions are strictly confined to a defined subspace where participants communicate on a face-to-face basis. However, with the advent of computer mediated (and other tele)communication, the very nature of our day-to-day interactions have been fundamentally altered such that we are no longer limited by time or distance. Moreover, this paradigm of interaction is nowhere more prevalent than in a Massive Multiplayer Online Game – or MMO for short.
In a MMO, such as World of Warcraft, there exist social structures known as guilds which consist of large collections of members and are formally organized with leadership positions. In a study by Einar Stennson, he attempted to elucidate some of the social characteristics of an MMO guild through an examination of reciprocal relationships among members of the guild.
Using the graph abstraction that we discussed during the Graph Theory and Social Networks topic, each member (node) was asked to rank their connection to another member on a 1 to 5 scale (represented as a one-directional edge). The net strength of each relationship was quantified by the minimum value of the tuple of scores from two members; for example, a score of (5,5) between two members indicates a very strong connection of rank 5, a score of (1,1) indicates a neutral/weak connection of rank 1, and a score of (1,5) indicates a rare, unbalanced connection of rank 1. The in-degree – the number of incoming edges from other nodes – of each player/node represents the number of relations a member is involved in.
The study ended up finding unsurprising, yet interesting conclusions (given our knowledge in the subject) about the social structure of a typical guild. In a sociogram/graph of relationships with rank 5, the number of participants with a high degree of relations were distributed about the central core of the graph whereas the participants with low in-degree were located about the periphery of the graph with one or two connections. Those with larger in-degree were generally members with higher amounts of time spent with the guild and vice versa. Moreover, if we define a connected component to consist of nodes that have at least two relations from another member of the component, there exists only a single, giant connected component in the graph which suggests the new members haven’t really connected with the guild just yet.
The complementary graph is just as enlightening: in a graph of relations of rank 1, those with the highest in-degree were the newest members and vice versa. Furthermore, there wasn’t a single connected component in this graph which suggests that those with rank 1 relationships haven’t really bonded yet either.
Tying this data to lecture and from chapter 2-3, some of the knowledge that we learned about graph theory and social networks in CS 2850 are extremely relevant in understanding this data. From what we can glean, it is clear that there is a positive correlation between time spent in the guild and the number/strength of your relationships. This is linked to our discussion on triadic and strong triadic closures: that given enough time, points of stress among members are resolved when mutual friends begin to connect. The same thing can be expected to happen in the guild: that given enough time, the newer members will begin to form stronger and more relationships (forming triadic closures) and join the giant connected component een in the first graph! There should be less members on the periphery of the rank 5 graph and a steady decrease of nodes from the rank 1 graph. And, from our discussion on connected components, in a large, constantly interacting population, either these members will join the main core of the guild … or leave and join a different guild! For anyone who has played an MMO before, this is phenomenon is extremely familiar!
www.diva-portal.org/smash/get/diva2:224891/FULLTEXT01
Targeted Advertising in Networks
One of the main issues any social media site will face is how they will raise revenue. Most of these services are free, but in order to continue running the business, some source of money must be coming in the door. Twitter is launching a new program that will match advertisers to customers. Marketers will be able to identify and, specifically, target users who align with the business’market. This will allow the advertisers to save money by foregoing mass marketing techniques and implementing a more targeted strategy. In the article from Businessweek presented below, the authors note the financial benefits of such a program by comparing it to a similar service from Twitter’s competitor, Facebook. Twitter’s plan mirrors our class discussion on matching markets and bipartite matching. All bipartite graphs are divided into two categories; advertisers and users in this situation. The nodes are the individual users and advertisers. Anedge exists when an advertiser connects with a specific user based on the content of their tweets. An edge can produce economic value when it leads to a click from the user. There is no perfect matching scenario because multiple advertisers can be linked to one user and the user can click on multiple ads without creating a constricted set.
Preference is also a very important concept in conversations about matching. In almost all situations, users are not completely indifferent to all options. In the case of Twitter, users value certain ads over other ads. Therefore, these users will have some set of valuation over the presented ads. This preference set will affect which ads they click on and, thus, which companies will make money. Although this example differs from class in the sense that no possibility of perfect matching or constricted sets exists, it is still a great case of networks creating social and economic exchange.
http://www.businessweek.com/news/2013-05-23/twitter-is-said-to-ready-customermatching-tool-for-advertisers
Predicting Egyptian Turmoil with Game Theory
http://www.cnn.com/2013/07/07/politics/egypt-predictive-analysis/index.html?iref=allsearch
Ever wondered how game theory can be applied large-scale? I’m not just talking about an interstate highway system. I’m talking about applying game theory to an entire country, and that’s exactly what Mark Abdollahian and other political scientists at Senturion have done. What’s more, the predictions from their model (made in 2011) have come to fruition. The predictive power of a model using game theory such as this is intriguing. The model was able to correctly predict that the military in Egypt would allow some democratic elections, but it would also remain the undisputed center of power in the country for the near future. The model also continues to make predictions. Although the purpose of the model is primarily to predict the power structure in Egypt, the scientists were also able to draw conclusions about the impact of
the power structure. For example, Abdollahian’s report stated that the military would hinder antiAmerican extremism. Game theory models such as this can be applied to other countries as well, and that’s what makes this idea interesting as well as powerful.Upon closer examination, this “game” is just a scaled-up version of the games we’ve looked at in class.
In chapter 6, we looked at games primarily composed of 2 players with 2 possible strategies and a payoff for each possible strategy. With so many players (politicians,militants, etc) and different voting strategies in our model of Egyptian power structure, there is almost certainly no strictly dominant strategy for the players. Also, there are probably no Nash equilibria, as it is unlikely that there is a mutual best response when so many players are involved. Rather, there is a mixed strategy equilibrium that is calculated from probabilities of the many different outcomes. The mixed strategy Nash equilibrium is determined with a computer program, and the most likely outcome is the prediction of the model. It’s cool how the concept of game theory that we learned about in class is being used to model bigger and more advanced systems.
Segregated Cities and Schelling’s Model
This link attached is a census map of America’s top segregated cities. It focuses on the continuing high levels of segregation seen in American cities and ranks twenty one highly segregated cities in terms of a number called the dissimilarity index, which is defined by the article as the “percentage of one group that would have to move to a different neighborhood to eliminate segregation” (Baird-Remba, 2013).
This article is interesting in that it offers some very surprising statistics regarding how racially segregated some cities in America are today. It also tells us which particular racial groups are most segregated and provides local maps of these cities that color code the different racial groups residing in the city, which is also very interesting in that it reveals some details about the demographics of the city.The article relates to Chapter 4, Section 5, of Networks, Crowds, and Markets. The section is mainly about the Schelling Model, which explains how local regions can become very segregated even when no government entity or individual explicitly enforces segregation, indicating that the remaining forces driving segregation are very strong. As described by the Schelling Model, the segregated regions are comprised of mostly people with very similar characteristics such as race, ethnicity, or culture. This is reflected in the article linked below, as the census map illustrates deeply racially divided cities. Lastly, the fact that there exist intensely racially divided cities today supports Schelling Model’s claim that the forces driving segregation are very strong. The article is thus relevant in that it provides some concrete facts that relate it to the Schelling Model.
Link: http://www.businessinsider.com/most-segregated-cities-census-maps-2013-4?op=1
Social Norm versus Nash Equilibrium
http://www.post-gazette.com/stories/opinion/perspectives/applying-game-theory-to-syria-702675/ebPreServing/
Game theory is designed to address occurrences in which the outcomes of a person’s decisions depend not only on how the choices they make, but also on the choices made by the people with whom they interact. In Kevin Zollman’s article of Applying game theory to Syria he questions United States’ decision making on addressing the use of chemical weapons in Syria. President Barack Obama decides to call for missile strikes after reports of Syria use of chemical weapons that killed 1,400 people. However, Mr. Zollman questions this as an irrational decision that even though there were 100,000 deaths by conventional weapons, America only now intervenes when there are only 1,400 deaths.
A reasonable argument for intervening is the peer pressure against the use of chemical weapons. Mr. Zollman pointed out that this game is divided in three groups: first are those who follow the norm because of fear of punishment, second are those that will not follow the norm when their opponents don’t, and lastly there is a group that follows the norm regardless of others’ actions. In this case, because Syria is not following the “norm” by using chemical weapons, if Syria continues without punishment, according to game theory, other parties’ (countries) best strategy is also to use chemical weapons as well. To explain this, let’s look at a simple model where you (A) and your opponent (B) are in a game where you both make a decision at the same time without knowing what the other person is doing. The trade offs are illustrated below. If your opponent uses chemical weapons, the death rate in your army (or pain) will be higher in A than in B, and vice versa if A uses chemical weapons and B does not. If both sides do not use chemical weapons (hereafter abbreviated to CW), then the death rate will be half as much. And lastly, if both sides use CW the death rate will be a bit more, but not as much if only one side uses chemical weapons. If B decides to use
CW, then A’s best response is to use CW; if B decides to not use CW, then A’s best response is still to use CW. In addition, regardless of what A decides, B’s dominant strategy is also to use CW. This will create Nash equilibrium of both sides using their dominant strategy: Use Chemical Weapons.
The Use of Chemical Weapons
You\Opponent Use Not Use
Use -3, -3 -1, -4
Not Use -4, -1 -2, -2
Thus, in the context of Syria, if Syria goes unpunished for the use of chemical weapons, other countries’ best strategy is to also use chemical weapons. Zollman says “Those leaders [in the first group…] will try to get away with it. This, in turn, will lead [the second group…] to use chemical weapons because they fear being taken advantage of by a malicious opponent. Eventually, chemical weapons might again become a common occurrence in war, as they were in World War I” The game theory associated to United States’ decision to intervene with Syria relates to what was taught in class because it ties to what are the best responses, dominant strategies, and Nash equilibriums of following the “social norm.”