This BBC video describes the situation of identity theft by the social networks we create via Facebook. As we all know Facebook is filled with many applications to keep in touch, pass the time or procrastinate with; but something we probably never think about is the chance of becoming a victim of identity theft by simply using an application, or if 1 of our hundreds of friends use an application. The BBC was able to create an application that would steal users information in their profile and the information from their friends profiles. The BBC has looked into Facebook’s user agreement and it states that such actions could occur and that their team is doing everything possible to remove such applications, but how long do such applications take to steal this information and how long will it be before Facebook’s tech team finds the app and puts an end to it?

This flaw gives people the opportunity to get information from people they would otherwise not be in contact with. They do not need to message or become the persons friend. All that is needed is to share a common friend and with the ease of adding friends you never know who you are connect to. This serve a prime example of the six degrees of separation. A direct path from node A to B is no longer necessary, but with a little ingenuity one can find an alternate path leading to the desired information.

http://news.bbc.co.uk/1/hi/technology/7376738.stm

http://www.steve-jackson.net/six_degrees/index.html

There are few fields that reveal the power of networking than in business. Without a network of referrals or contacts, it’s difficult to make headway into a new industry, especially when the industry is filled with established businesses. With a bit of help from someone who plays golf with the CEO of a shipping company or who was childhood friends with the director of the supplier, a budding business benefits greatly from a good network. The strength of weak ties allows the entrepreneur to have access to resources not otherwise available to them.

A network must be properly maintained, however, in order to be effective. The edges will not be useful unless your connected nodes are motivated to help or unless they are informed about your business. The stronger the tie, the most useful the contact, so it’s necessary for there to work closely with them in order to get the best results. The gatekeeper or bridge to other networks makes it much easier to reach other people and other resources, rather than having to go through other paths.

http://www.msnbc.msn.com/id/23222279/

In my last blog, I investigated the time taken for a giant component to develop in a social network.In that experiment, when the largest component contained the majority of people in the population, I stopped the simulation and recorded the time taken. If I were to continue the simulation, we’ll observe that the giant component eventually expands to include almost all nodes (persons) in the network. The size of the giant component thus converges to a constant over time as shown on the graph below for a virtual world of 1000 people:

In future experiments, I would like to extract statistics from the virtual world after this giant component has achieved equilibrium. I thus need a way to automatically detect when equilibrium is achieved in my virtual world. In this blog, I’ll explore how I implemented this, and I’ll also investigate the factors that affect the time taken to achieve equilibrium.

First, I need to clarify exactly what I mean by the term “equilibrium”. A social network is in equilibrium if the probability that the giant component grows is equal to the probability that the giant component shrinks. At the start of my simulation, due to the sparse nature of the network, the probability that the giant component grows is very high. As the simulation runs, the network gets saturated with friend connections and the probability decreases. At some point, the probability will decrease to 0.5, upon which we have reached the equilibrium point.

Now that I know exactly what I mean by equilibrium, I need to determine how I can detect it. Consider the graph above that shows the growth of the giant component. It is obvious that equilibrium has not been achieved in the first 300 days as the size of the giant component almost monotonically increases every day. The approximate plateau from day 400 onwards also indicates that the size of the giant component is stable, and thus the system is in equilibrium. We can thus estimate that the system is at equilibrium at day 400. Unfortunately, its is a bit harder to teach this visual recognition to a computer simulation. For the purpose of simplicity, I’ll assume that when the giant component is at equilibrium when it contains at least 90% of the population. I ran a few simulations to confirm the validity of my 90% heuristic.

After adding equilibrium detection to my simulation, I examined the relationship between the time taken to achieve equilibrium, and the average time taken to make a friend in the social network. The result of this simulation is shown in the graph below:

The relationship was linear. The time taken to achieve equilibrium is directly proportional to the average time taken to form friends. The constant of proportionality was 5.0.

Conclusions :

If E = time taken to achieve equilibrium, and T = the average time taken for a person to make a friend :

E = 5.0 T

Using the result used from my previous blog , we can also establish the relation between E and L (the length of time taken for the giant component to form) :

E = 2 L

This surprisingly simple relation says that the time taken for a system to achieve equilibrium is exactly twice as long as the time it takes to for the giant component to form. This result has some interesting implications. For example, consider a new instant messaging service. If this service measures the time it takes for a giant component to form within the network, it can accurately predict when the network will fully develop. This type of information can be exploited for strategic commercial planning.

My simulation source code can be found here (Visual C++ 2005).

Oracle of Baseball (http://www.baseball-reference.com/oracle/) uses a database of every MLB player to track how “connected” different players are to each other. It attempts to link two different players using common teammates. For example, I could type in Cy Young and C.C. Sabathia (the 2007 AL Cy Young Award winner) and I will be shown the fewest number of steps to connect them. This example results in 7 steps, which seems like a lot at first…until you realize that Young retired in 1911 and died over a half century ago. This shows not only how connected the current baseball landscape is, but also how closely linked baseball is to its heritage.
Certain players that played for many teams (such as Rickey Henderson) or played for many years (like Julio Franco) serve as common links between many players. However, the Oracle allows you to eliminate certain players to find other paths. Therefore, a three step link through Henderson may have another route around him, possibly requiring more steps. This shows that local bridges are almost always not the sole way to link different parts of the network.
This site is a fun database to play with, and the results are not surprising to anyone familiar with the small world phenomenon.
In case you wondered, it’s 6 links from Alex Rodriguez (2007 HR leader) to Jim O’Rourke (1880 HR leader)

The market of lemons can be witnessed almost in any economic market. More specifically, asymmetric information between sellers and buyers exists where one party holds more information than the other. The information problem can either cause an entire market to collapse or contract it into an adverse selection of low-quality products. This knowledge allows that party to find strategies to favor their personal endeavors. Some examples that stream from this idea are startup companies, insurance buyers, manufacturers, stock market, etc.
According to the article, “The Real Reason for Lemon Laws”, the market of health insurance is an excellent example of the market of lemons. There exists substantial information asymmetry between the health insurer and the customer. The customer has a clear advantage for gauging his/her own personal health. In response to this informational disadvantage, insurers have begun to increase the premium rates in order to account for the increased chance of insuring very sick individuals. Soon it becomes risky to purchase the health insurance policy due to the increased rates. The bad (sick individuals) have driven out the good (healthier individuals). This dilemma of fairness between healthy and sick people has caught the eye of government policy. Currently, the government has funded programs such as Medicare, but they are still trying to solve the problem.
Health insurance is becoming problematic for many people. While 45 million Americans are without health insurance, the other part of the population with health insurance is sometimes dissatisfied with their health coverage. This is because health insurances have come to the realization that moral hazard (where one takes advantage of the system) is decreasing revenue. The health insurance market is plagued by two primary problems: moral hazard (consumers) and adverse selection (insurers). In response to these problems, health insurance companies have realized that healthy customers are good to cover, while some customers are bad to cover. The price of insurance must be low enough for healthy people to sign up. This is because insurance companies will generate money when healthy people purchase insurance but do not make claims. However, the price must be high enough to afford coverage for the unhealthy people who make a lot of claims. Overall, this problem is going to exist for a long time due to the money-driven insurers and intelligence of the consumers.

Reference: http://berkshireruminations.blogspot.com/2006/11/real-reason-for-lemon-laws.html

The market of lemons can be witnessed almost in any economic market. More specifically, asymmetric information between sellers and buyers exists where one party holds more information than the other. The information problem can either cause an entire market to collapse or contract it into an adverse selection of low-quality products. This knowledge allows that party to find strategies to favor their personal endeavors. Some examples that stream from this idea are startup companies, insurance buyers, manufacturers, stock market, etc.
According to the article, “The Real Reason for Lemon Laws”, the market of health insurance is an excellent example of the market of lemons. There exists substantial information asymmetry between the health insurer and the customer. The customer has a clear advantage for gauging his/her own personal health. In response to this informational disadvantage, insurers have begun to increase the premium rates in order to account for the increased chance of insuring very sick individuals. Soon it becomes risky to purchase the health insurance policy due to the increased rates. The bad (sick individuals) have driven out the good (healthier individuals). This dilemma of fairness between healthy and sick people has caught the eye of government policy. Currently, the government has funded programs such as Medicare, but they are still trying to solve the problem.
Health insurance is becoming problematic for many people. While 45 million Americans are without health insurance, the other part of the population with health insurance is sometimes dissatisfied with their health coverage. This is because health insurances have come to the realization that moral hazard (where one takes advantage of the system) is decreasing revenue. The health insurance market is plagued by two primary problems: moral hazard (consumers) and adverse selection (insurers). In response to these problems, health insurance companies have realized that healthy customers are good to cover, while some customers are bad to cover. The price of insurance must be low enough for healthy people to sign up. This is because insurance companies will generate money when healthy people purchase insurance but do not make claims. However, the price must be high enough to afford coverage for the unhealthy people who make a lot of claims. Overall, this problem is going to exist for a long time due to the money-driven insurers and intelligence of the consumers.

Reference: http://berkshireruminations.blogspot.com/2006/11/real-reason-for-lemon-laws.html

http://www.sciencedaily.com/releases/2008/04/080428094212.htm

A Nash Equilibrium is reached when people discover what choice will result in the greatest individual benefit in a game.  In team reasoning, however, people act in the best interest of their team, as opposed to the individual. This article talks about a recent study that set Nash Equilibria and team reasoning against each other.  The study showed that in some games, team reasoning was a better predictor of behavior than the orthodox game theory Nash Equilibrium.

This study is interesting, but not altogether surprising.  It highlights “flaw” in humanity that sometimes puts a team over individual self-interest.  It is that very trend in humanity, however, that allows us to create functional families, communities, and nations and prevents a “Lord of the Flies” type of chaotic situation from dominating human society.  

http://www.newsweek.com/id/134920

In this article, researhers from the University of Maryland, Duke, and Johns Hopkins used game theory to predict levels of parental discipline.  They found that parents really do become less strict with younger children and the effects show.  Parents are less likely to financially support rebellious older children if there are younger children at home, and having one more younger sibling causes a teen’s high school drop-out rate to go down about 3%.  Younger children, with lessened parental discipline are more likely to engage in risky behaviors like unpredicted sex, smoking, and drinking. The article suggests that the reason parents are stricter with older children is that they want to prevent older children from setting a bad example for younger ones.  By the time younger children run into similar issues, parents respond with love instead of discipline, so younger children don’t need to fear severe consequences or rejection from parents.

The article’s main motivation for strict regulation with older children is that parents have to keep order in the house for the sake of the younger children.  Although this may be a part of the parent’s motivation, another factor could be the parent’s unfamiliarity with facing a particular issue.  If, for example, a parent discovers that the oldest child in the family has started smoking cigarettes, the parent, knowing how destructive the behavior is, will be very upset and concerned and may impose severe consequences on the child to try to stop the behavior.  If the attempts to stop the first child were unsucessful, the parent may reflect that their strict response was unsuccessful and only added tension to the relationship.  Then if a second child starts smoking, the parent will still be very upset and concerned, but may be less harsh with the second child to preserve the relationship. So, parental leniency with younger children may be caused by experiences in earlier “trials” as well as the absence of younger children at home that need a clear example.

Stephanie Rosenbloom of the New York Times wrote today on new features of familiar social networking sites like Facebook, Friendster and MySpace. She writes that these websites are increasingly becoming platforms for job searching and professional contacts. Modernizing Mark Granovetter’s hypothesis in his paper “The Strength of Weak Ties” - that many people actually find work through weak ties in their social networks - Rosenbloom suggests that these modern social networking websites are facilitating a link directly between an employer and a job searcher. Rosenbloom cites the job search website, CareerBuilder.com as among the new job search Facebook applications which allows companies to find potential employees on Facebook. Perhaps Facebook is taking a lead from LinkedIn, the professional networking website that Rosenbloom cites as the website that executives are most interested in recruiting from. One company’s communications director in Rosenbloom’s article got his job through LinkedIn, and even turns his virtual social network into a physical one, when he organizes “LinkedIn Live” meetings for candidates and employers that are connected on the website. As noted by this executive, social and professional networking sites like LinkedIn, and now even Facebook or MySpace, are increasingly forging ties between employers and job candidates. It seems that many of the connections formed via these networking sites might never have occurred otherwise, allowing for greater and broader opportunities for online networkers in terms of job searching. Rosenbloom suggests that perhaps we no longer need to reach out to the “weak ties” of our network when we are in need of work, à la Mark Granovetter, but can simply place ourselves in one of the newly developing professional networks like LinkedIn and make our own connections.

So a classic problem that wasted hours of my life when I was younger:

You have three houses: A, B, and C. Your goal is to connect them to three utilities: Water, Gas, and Electricity (W, G, and E)… but none of the lines can cross. It turns out this is impossible if all 6 nodes are in a plane. Go ahead, try it out, I’ll wait. Here, here’s somewhere to practice:

W G E

A B C

so the reason is that the graph K_{3,3} (the bipartite graph we’d achieve if this was doable) is not planar. The proof of this relies on Euler’s theorem for planar graphs, which says that for any planar graph

R + N - E = 2

where
R is the number of closed regions
N is the number of nodes
E is the number of edges

For K_{3,3}, clearly N=6 and E=9, so we would need to have R=5. A closed region is an area bounded by a cycle. For example, if we were to connect A–W–B–E–A that would give us one region.

So, suppose there were 5 regions in K_{3,3}. First, notice that we don’t get a region with a cycle with two edges, since that simply means we used the same edge twice. Also, there are no odd cycles in a bipartite graph, so any region must be bounded by a cycle of at least 4 edges. However, each edge will be a member of a cycle for two regions (one on each side) so this means that we need 5*4/2 = 10 edges in order to have 5 regions. We only have 9 in K_{3,3} so this is impossible.

http://www.cut-the-knot.org/do_you_know/3Utilities.shtml