During our first few days of studying game theory, Professor Easley alluded to a study done on professional tennis matches that was similar to the Palacios-Huerta paper we read about the von Neumann Minimax Theory in professional soccer. You can find it at http://www.u.arizona.edu/~jwooders/WimbledonAER.pdf – “Minimax Play at Wimbledon” by Mark Walker and John Wooders. This is another situation in which the players of the game are highly motivated and rational.

Walker and Wooders explain that every point of a tennis match can be turned into a 2 x 2 game just like the ones we have been studying. The server of each point has two options: to serve to the right side or the left side of the returner. The returner, they claim, guesses to which side the serve will go. One could debate that a significant portion of service return involves reaction rather than guessing. Though they don’t state it explicitly, the writers appear to recognize this by approaching their analysis from the server’s point of view and neglecting to mention the returner even once after their initial explanation of the game. (Plus, of course, it is impossible to watch a serve and know which way the returner guessed). They also distinguish between four different types of games within each match. In tennis there is a deuce-side serve and an ad-side serve and the strategy and mental processes behind each is different. Then two more games can be made by analyzing the game of both serving sides by reversing the roles of the server and returner.

Anyhow, what they did was take ten high profile grand slam matches and computed (for each of the four games) the frequencies with which the server served to each side of the returner, the probability of winning a point on each side, and of course the success rates of serving to each side. As I understand it, these success rates are what the Minimax Theory says should be equal on each side. In many cases they are, but this data is not nearly as convincing as that of Palacios-Huerta. Have a look at page 1526 (6 of 18 in the pdf) for all of this data. That is the most important page you could look at. The data looks decent (the matching of the Win Rates column).

This brings up a discussion that Dr. Easley touched on that there are many more variables in this tennis situation than in the soccer one, even though the players of each game might be equally rational. First of all, even discounting the direction of a serve, it still has many variables such as the speed and spin. Also, serves and returns happen all throughout a tennis match (penalty kicks in soccer are only at the end and are all equally crucial). So the players may gamble more at certain times compared to others (in other words there’s a lot more involved mentally at any given time; then again perhaps all of the extra thinking helps the players achieve Minimax values). Walker and Wooders try to compensate for variability by creating as much isolation as possible. This is why they looked at the four types of games separately and looked only at matches between players who knew each other’s games well.

On the other hand, the extra data we get by looking at tennis can be an advantage. These serving games can be looked at among players of all levels since serving is highly integral to the sport. It would be easy to conduct this same study among high school or college players to see how well their win rates match each other. The skills of non-professional players tend to be skewed: they have more exploitable vulnerabilities and fewer strengths (shots and tactics at which they are much better compared to other shots and tactics).

This same study might be interesting if conducted among female professionals, who serve slower than the men do (due to wing- and shoulder-span, meaning that it would be less of a game involving simultaneous strategy selection and depend more on reaction. It would still be a similar game from the server’s perspective because there would still be different probabilities of winning the point when serving in each direction.

A final study that might be interesting is a longitudinal examination of one or few rivalries between players. Andre Agassi and Pete Sampras faced one another about 30 times (professionally; even more as juniors), many of which had implications just as great as those of the matches Walker and Wooders use. The logic behind the longitudinal study is that the players become even more rational and motivated as they learn the best ways to play against one another.

Here I have chosen to analyze the overly simplistic model of the US interstate system (found at the link below) in terms of graph theory. I feel that several insights about networks may be gain by such an analysis despite the oversimplification already noted. Each city should be viewed as a node and each highway as the connecting edge. The conclusions drawn here are obviously not fully representative of the many factors that determine a city’s commercial success, but rather interesting considerations to entertain.

This diagram comes from an artist, Chris Yates. http://www.chrisyates.net/reprographics/index.php?page=424

First, consider a concept such as betweenness. Dallas or Oklahoma City have large betweenness values in this graph which I will not attempt to calculate but would like to compare to other cities such as Fort Myers or Nogales. These two cites have a betweenness value of 0 and I personally rarely hear much about them. It is interesting to consider the possibility that Dallas’ and Oklahoma City’s large commercial success relative to Ft. Myers and Nogales may, in part, be the result of their large betweenness values. They are an intermediary in the route to numerous cites providing them with a large amount of commercial traffic; however, in the case of Nogales and Ft. Myers each of these cities must be a destination rather than a checkpoint.

Obviously, this cannot be true for all cities. San Diego for example has a betweenness value of 0, yet, as a city, it is a large commercial success. But, here it should be noted that
the graph only represents potential land commerce by way of the interstate system. San Diego is also home to an international airport and is a seaside city.

It is also interesting to examine this graph with regard to power relations within social networks. These are cites instead of people but they often interact, trade, and rely on one another in much the same ways that people do. Chicago is the intersection for six major interstates. Grand Rapids on the other hand has only two interstates to work with, 65 and 96. By comparison, Chicago is in a far more powerful position in terms of potential interstate commerce.

Most of the nations’ most powerful cities are found on this graphical representation. While much of this is by design, it is also indicative of the importance of connectivity for being a major center of commerce and industry. And, after all, it is a cool picture.

http://www.washington.uwc.edu/about/faculty/muryn_j/ECO%20203/16th_edition/wsj101504vengeance.pdf

Most examples of game thoery discussed in class are primarily concerned with players maximizing their payoff; however, what if we were to introduce a new factor in which players had the option of attacking other players based on their actions? This articles addresses the reasons behind the drive for so many individuals to take action into helping the poor and contributing to humanitarian efforts.

On a completely Machiavellian scale, one would assume that helping those in need had somethign to do with advancing some personal agenda in which they would be compensated for their efforts. The problem with this comes in the form of the “Good Samaritan” in which he desires no compensation and acts out of “pure altruism.” This idea of pure altruism makes little sense in economic theory as there seems to be no motivation in doing so; however, scientists have discovered that there is indeed a plausible motivating factor in altruism. “There are just enough people in society who are willing to punish anyone who does not contribute to the common good, even when it costs them to do so. Scientists call it “altruistic punishment.” But you can think of it as righteous vengeance.”

The articles goes on to explain a game in which there are multiple players who have the option of contributing a certain amount of money to a given cause in which they will be compensated double their contribution. The problem with this is freeloaders who contribute nothing but feed off of the generosity of others. An added option is the ability to punish other players at the cost of the attacking player. This seems to make no sense in economic theory as nobody’s payoff is being maximized but is infact being lowered. In many cases, it was found that the willingness to punish was nominal. The fact that these “avenging angels” are in the game make an incentive to contribute in order to escape punishment.

With regards to social networks, it could be best be summed up in the statement, “would-be freeloaders get the message that, if they fail to contribute to the common good, someone out there may nail them for it”

http://delivery.acm.org/10.1145/1070000/1064010/p1-altman.pdf?key1=1064010&key2=1714043711&coll=&dl=ACM&CFID=15151515&CFTOKEN=6184618

-or-

http://portal.acm.org/citation.cfm?id=1064010&dl=ACM&coll=&CFID=15151515&CFTOKEN=6184618 (Click on full text PDF)

This article discusses ranking systems, specifically Google’s PageRank. An analogy between page ranking and social choice is examined. Page ranking is compared to agents (pages) preferring other agents (pages). This preference on the internet is found in links between pages.

The paper states that “the current practice of the ranking of Internet pages is based on the idea of computing the limit stationary probability distribution on the Internet graph, where the nodes are pages, and the edges are links among the pages.” This basically means that the result of the search is similar to starting at a related page and than following random links iteratively from page to page. If this procedure is repeated, the pages most often visited should rank the highest in the search results.

The goal of the paper is to find a small set of simple axioms that do not require complex mathematical computations; these axioms should be found in good ranking algorithms.

One axiom discussed is isomorphism, which says that the ranking system should not depend on what the names given to the actual pager are. Another axiom is called “Vote by Committee” and says that if a page (call it a) links directly to two other pages (pages b and c), the same relative rankings should be given to all pages as in the case when a links to another page d that only links to b and c. Another axiom is called “Collapsing” and says that if a set of pages links to a and b, and a and b in turn link to another set of pages, this is equivalent to collapsing a and b into a single node. The paper goes on to prove that these and a few other more subtle axioms are satisfied by Google’s PageRank ranking system.

In the authors’ conclusion, they state that more work is clearly needed to “isolate the ‘essence’ of particular ranking systems,” but the paper does a good job at getting at some basic axioms that should be satisfied by successful ranking algorithms.

http://news.com.com/Facebook+goes+corporate/2100-1038_3-6066533.html

This article covers Facebooks new ventures of social networking. Facebook is a website that has been used in the past for Students at both the high school and college level to stay connected. Now facebook is attemting to cover new waters as it is now allowing a select few companies to use facebook as a networking tool. Before you had to have a .edu website and they are now allowing .com and .org addresses. Facebook saw that users had secondary email addresses as places that were assumed where they work. With so many requests for facebook to allow people outside their network to the site and haveing nearly 50 percent of their graduating seniors visit the site everyday they decided on this new change.

Facebook is one of the many social networking sites that are all over the internet just like myspace and Xango websites. The only difference is that facebook only had students allowed to join. Sites like these are prime web examples that we have been through in lectures. As this fits the description perfectly with each node represented as a person and each edge represented as a “friendship.” Many friends are able to keep information flowing back and forth between the two as this is not a directed graph. Now with the new companies coming in this will allow even more information to be able to flow connecting employess of the companies and also allow information from companies to be accesible from students who might be going out the real world of work.

I think Facebook now going into the business world is a great addition to their site. As long it becomes a decent hit within the companies that are being allowed to create profiles then I believe these additional nodes will benefit both the student world and business world. Although, as the article mentions, this could hurt sites that are meant to be networks between jobs and job searchers. I think this will eventually catch on and a whole new world will be created between all nodes(users).

Paul Erdős (1913-1996) was one of the most prolific mathematicians of all time, having written about 1500 mathematical articles during his lifetime, mainly with co-authors. Due to his immense output and large number of collaborators (numbering 509), the concept of the Erdős number was concieved as a way to describe the “collaborative distance” between authors of mathematical papers. For example, Erdős himself has an Erdős number of 1; a coauthor for one of his papers would have an Erdős number of 1; someone who has collaborated with a person with Erdős number of 1 (but not with Erdős himself) would have an Erdős number of 2, and so on. In other words, an Erdős collaboration graph can be drawn with paper authors as nodes and the papers edges. The Erdős number is then the shortest path from a certain node to Erdős himself.A more interesting way to look at the Erdős collaboration graph was suggested by Michael Barr ofMcGill
University in his article Rational Erdős Numbers (http://www.oakland.edu/enp/barr.pdf). He proposed that instead of simply assigning an Erdős number of 1 to each of Erdős’ direct coauthors, we can look at the exact number of papers they have collaborated on and take the reciprocal of that. For example, a person, A,  who has coauthored 4 papers with Erdős will have an Erdős number of 1/4. Lets say another person, B, then coauthors 3 papers with A. His Erdős number will be 1/4 + 1/3 = 7/12. Letting the Erdős number have non-integer values based on how “closely connected” each person is to Erdős and his collaborators makes the task of computing the Erdős number infintely more complex, especially when we consider the fact that many of the collaborators have collaborated among themselves.Michael Barr then suggested a remarkable physical interpretation of the graph. He proposed that we replace the edges between nodes with 1 ohm resistors. The Erdős number would then be the effective resistance between Erdős and the particular node in question. The network can be analyzed using a set of simultaneous equations given by Kirchhoff’s laws. It is interesting how modelling a social network between people as an electrical network simplifies the picture and enables us to have a more intuitive grasp of the network. It is noted, however, that although this allows us to use established electrical laws on the network, computing such a large number of simultaneous equations may not be practical.     

http://www.americanscientist.org/template/AssetDetail/assetid/45930/page/1

          Game theory is a concept that applies to not only humans but also to any biological population in the world. It has been used since the beginning of time, starting with the first species to inhabit the earth: viruses. In this article, two scientists undergo experiments to test their predictions that viruses have a dominant strategy of “cheating” or taking advantage of other species to undergo selfish profits. This claim is very similar to the prisoner’s dilemma game, in which the equilibrium strategy for both players is to confess, or cheat the other person so as to gain freedom or the highest payoff.

         Their experiments involved a population of RNA viruses called phi-6, and a bacterial colony called P. Phaseolicola. They created six separate samples; three of them contain both the RNA viruses and the bacteria colonies which are allowed to co-infect each other, while the other three consist of both the virus and the bacteria such that a virus can only infect a single bacteria cell. After, 50 days, or 250 generations of bacterial growth, the six samples were taken for observation. The scientists found that the viruses that were allowed to co-infect had greater viral fitness than the ones that were only allowed to infect a single cell. Furthermore, the viruses that were able to co-infect evolved their genotypes so that they could efficiently use the resources of other viruses while keeping its original key genes. These were called the “cheaters.” It was also found that there were viruses in the co-infecting environment that did not evolve, which were named the “cooperators.”

           To further test their claim, they performed tests that consist of varying amounts of evolved viruses and ancestral, or unchanged, viruses. Eventually, they found that as the population of evolved viruses decreased in size, they tend to take advantage of the cooperators and infect them. On the other hand, if the population of “cheaters” increases, they had to infect each other. This shows that the fitness of the evolved viruses depends on the frequency, or the amount of competition that occurs within a community. It also shows that through time, the evolved viruses will emerge dominant over the ancestral viruses. In conclusion, the equilibrium strategy for viruses is to cheat.

This matrix sums up the kind of game that viruses play with each other and with othe species. What is interesting to see is how the behavior of viruses can be related to the behavior of other organisms, or even people. In the end, will the defying dictators of the world succeed, while the cooperators weaken? Will the selfish people be destined to become better off than the caring, cooperative people? Also, how can this game be changed so that the social welfare of both players increases?

M-Dot Strange Finds a Way at Sundance

“M-dot Strange” is a 27 year old from San Jose, CA who has been making a movie titled “We are the Strange”. Before reading the article, the movie and the director had no relevance to me, but as someone who is interested in Sundance, I was introduced to both, thanks to the power of ‘Triadic Closure”. According to the Gueorgi Kossinets and Duncan J. Watts article we disussed earlier this semester, Triadic or Cyclic closure is defined as the “probability that two previously unconnected individuals who are…apart in the network will initiate a new tie”.

The above New York Times article discusses how an unlikely candidate named “M Dot Strange” found his way into this year’s Sundance Film Festival. According to the article, over the last two years the self-titled writer, director, animator, and effects coordinator “has been posting a video blog on YouTube letting people know how the movie was coming along. And then two months ago, he finally posted a trailer, and almost immediately it was downloaded hundreds of thousands of times.” Since the article was written in January, I was curious to see how many viewers there had been since it was written. What was some 648,000 at the end of January, has become 741,500, meaning that almost 100,000 viewers a month are watching the trailer to M-dot Strange’s movie. The vice-president of YouTube, Kevin Donahue is quoted in the article as saying: “The originality of the work is quite high, but he (M-Dot Strange) has also built a real rapport with his audience. He has an online film school and a very active community.”

The fact that one person with access to the Internet, in a matter of two three months has created a network with more than 741,000+members I find to be fascinating. I thought about how a network of this magnitude is established, and it occurred to me that the idea of Focal Closure was at the center. Obviously of the 741,000 views, a vast majority of the views were from people who had the common interest in movie or film watching (or at the very least online web viewing). Thus, because of focal closure, people who enjoyed watching movies found their way to this trailer. But if we think about how many different types of film genres there are, we have to realize that not all of the viewers were interested in freeze-frame animation, this movie’s genre. Hence, M-Dot strange must have realized that if he were to create a community with large numbers, then the possibility of his freeze-frame film being noticed by people in the general film-watching network would become much more likely.

I thought this story was applicable to our class and the idea of Networks because it shows how if someone (a node) is isolated from other networks, then their opportunities to be noticed in those networks will be quite difficult. But if that node’s personal network grows, the opportunities to be included within those networks will undoubtedly increase. This concept (and thus this story) outline the phenomena of ‘Triadic Closure’ as well as “Focal Closure” we have read in the Kossinets and Watts paper earlier in the semester.

This recent article in the Globe and Mail describes a new social network being cultivated online: DNAancestryproject.com, a network that links people based on their related genes. This website is being run by Genetrack Biolabs, Inc., a DNA testing lab that has, until now, primarily focused on paternity testing and legal investigations. Those interested in becoming part of the network purchase a DNA testing kit, containing a cheek swab that they can send back to Genetrack. Once the cheek swab has been processed by the company, Genetrack returns copious amounts of information about the ancestry of the interested individual; depending on the desired, they will receive information about either their patrilineal heritage (available to men only), or their matrilineal descent (available to both men and women). Using this information, members of the site can learn more about the distant history of their ancestors, and more interestingly, find others in the network that share common genealogical heritage. While the test costs $119 for the most basic package, interest has been high, especially among those in middle age. Genetrack claims to have set up a network of over 300,000 active users, and, the higher the number of users, the more extensive and data-rich the network becomes.

What is most interesting about this phenomenon is that, if it gains enough traction, it may reverse current trends about the nature of the differences between family and friends. With most online social networking sites, a user can build massive friend networks comprised of complete strangers; with this DNA-based network, strangers are suddenly transformed into family members. With ethnicity and genetics being traditionally conflict-related subjects in the past, however, knowing a great deal more about a person’s genetic heritage could provide for new troubling types of discrimination and prejudice. Only time will tell whether or not this new experiment in DNA-based networking will be beneficial or detrimental.

Modern medicine and technology has undeniably made great advances for us–those lucky enough to enjoy its benefits. We now live longer and healthier lives, no longer needing to worry about many once-deadly diseases. We are able to screen ourselves and even our potential children for genetic illnesses. We are so optimistic about medicine that we’ve started to concentrate more on fixing and enhancing our exteriors, rather than insuring that our body works on the inside. However, one aspect of medicine that has remained at a relative plateau is psychiatry. With the advances of technology come more hectic lives and busier schedules, allowing less and less time for taking care of our own mental health. People are now more prone to breakdowns, and psychological disorders and diseases are as rampant as ever. How do we deal with affected individuals? Most of these afflictions have no known long-lasting cure. We put these patients into special institutions, away from society, so that they won’t disrupt the lives of the rest of us; we medicate their symptoms — turn them into virtual vegetables — claiming to calm their inner demons.

In many ways, the modernization of our culture has adversely affected those with mental health problems. Studies by the World Health Organization have found that in poorer, “third world” countries, the lack of our advanced medicine has been a blessing to people suffering from schizophrenia, a socially debilitating disease. Schizophrenia is a mental disorder characterized by an impaired perception of reality and significant social and occupational dysfunction. Those diagnosed with schizophrenia often experience hallucinations, disorganized thoughts, a lack of motivation, difficulty expressing and experiencing normal emotions, impaired psychological functions, and poverty of speech. Currently, apart from treating hallucinations and putting patients into psychiatric facilities, modern medicine in developed countries predicts limited chances of recovery. Basically, if you’re a schizophrenic in a developed country, if you’re lucky, you will likely live out the rest of your life in a psychiatric hospital, taking drugs to help you control hallucinations and possibly violent behavior.

According the “Social Network’s Healing Power is Borne Out in Poorer Nations,” a piece published in the Washington Post by Shankar Vedantam on June 27, 2005, the rate of recovery is much higher in poorer countries that lack psychiatric facilities and have very little, if any at all, medical intervention in the lives of schizophrenics. The article focused on schizophrenia in India, one of the countries where the World Health Organization ran a three-decade-long study that showed that schizophrenics fared better in these poorer countries, with significant rates of recovery, than in developed countries like England and the U.S. The difference in treatment in these poor countries is that for the most part, patients are encouraged to live normal lives. They spend very little time in hospitals, their care is by and the large provided by family members, and and doctors stop medications when the patients get better. Schizophrenics often have jobs, get married, and are in general more socially connected. According to the article, between half and two-thirds of the patients monitored in the WHO study became symptom-free, compared to only a third of the patients from rich countries.

The main point of the article was really the fact that it was the social connectedness that seems to be the reason the patients recover so much better in poor countries, where they often do not have benefits of modern medicine. Whereas in the U.S. a schizophrenic is prescribed drugs and a hospital stay, in India psychiatrists often recommend that families secretly pay employers to give patients fake jobs, so that patients have regular work hours, have the satisfaction of getting paid, and enjoy the social connections that are inherent in a work environment. It is the continuation of the patients’ networks that seems to be the key to the cure of schizophrenia.

While this article is only tangentially related to the material we covered in class, I thought it brought up an interesting aspect of the importance of social networks. Whereas we’ve been focusing on the strength of weak ties, and really the connectivity of weakly related individuals (auctions, buyers and sellers, the Internet), this article brings to light the importance of strong ties and a person’s social network in their health, a topic we haven’t really considered. While weak ties are a better way to spread information faster in a network, strong ties and just the continual existence of a network is linked to overcoming a debilitating psychiatric disorder like schizophrenia! Something interesting to consider is whether our culture is becoming too focused on a networks of weak ties, Internet-based relationships and connections where ties are formed by clicking on the “Add friend” button, where individuals very much still remain separate nodes. What are we losing by loosening the value of strong tie networks, where families are still a very central theme? Is our focus on the spread of information entirely beneficial and socially optimal?