On homework 3 there was a question about rational and irrational behavior of players in a game and how they influence each other. This on-line discussion reminded me of this problem and how game theory can be evolved over time to take various factors into account. The discussion can be found at: http://www.marginalrevolution.com/marginalrevolution/2008/01/logic-of-life-.html. The discussion starts from Fabio Rojas’s post. First, he gives a brief introduction to game theory and focused on Chapter Two of Tim Harford’s book, “Las Vegas: The Edge of Reason,” he introduces a broad range of applicability of game theory which ranges from poker, nuclear war, quitting smoking, to life saving. The part where I found the most interesting was about his criticism of game theory. He says although game theory does its best in suggesting the dominant strategy to go with and in predicting other’s behavior, its assumption that people behave rationally in their selection of optimal strategies is a lot to ask for. His example was strategies employed by world class poker players. World class poker players come up with their dominant strategies based on game theory-related analysis, but more based on trial and error. This is where he puts emphasis on an aspect of evolutionary process that game theory is lack of. According to Fabio’s argument, game theory is a fitting first step in understanding complicated interactions, but there should be an evolutionary theory of games that will serve better in predicting players’ behavior in a game. At the end, he adds a link to evolutionary game theory (EGT) for more information.

I also had a similar thought with his when I was first introduced to game theory. It was nice to be able to analyze the given payoffs and figure out which strategy would be the most advantageous. However, would people always implement their dominant strategy? I did not think one can take it guaranteed that one will always see rational behavior. Then, how can game theory be used if it is known that irrational behavior will take place? I had questions but no answers. I found Fablo’s point of taking evolutionary characteristics of human beings into account as an attempt to answer these questions very intriguing. It is true in a long run, human beings tend to show certain pattern in behaving and reacting to a situation. Focusing on the dynamics of strategy change should be able to tell something in predicting players’ behavior when the assumption of rationality does not exist any more. Fablo’s post was a good source in providing a general overview of game theory and especially in suggesting one of possible directions to take in order to improve shortcomings of game theory.

As the Democratic primary wears on, followers of the news have been inundated with reports about the special, uncommitted delegates who may end up playing a critical role in the nomination. These 796 “superdelegates” are national party members and elected officials who have been under intense media scrutiny and campaigns’ pressures to endorse. In a nation-wide race for a nomination, it is this select group that plays an important gatekeeper role. Their decisions can determine the outcome of the nomination and the future of their own careers. Delegates are under a great deal of pressure to support the candidate that they believe will be the best nominee and also to follow the will of their area’s voters.

In a slate article called “What’s a Superdelegate To Do?” [http://www.slate.com/id/2184677] Jeff Greenfield writes that delegates face down this choice philosophically and pragmatically. It is a game theory situation where the players must make their move uncertain what the others will do. If a delegate votes against the will of the people in his or her district they face severe scrutiny and pressure from hometown officials. They would hope that all other superdelegates decide to vote in a similar fashion so that they have political cover when they return home. Furthermore, the campaigns make the arguments that  voting the way districts voted benefits Obama, while voting the way that previous arrangements and concepts of best leader (which also contains a good deal of self-interest by the delegate for favors or fear of reprisals) benefits Clinton. So the superdelegates must hope to play the game the same way most others do so that their candidate is the eventual nominee. If they play the game differently than others, say by favoring Obama when the rest go to Clinton, they risk the strain in relationship with the supporters of the future president.

The article mentions John Rawls’ “veils of ignorance” which must be used when playing this game. Considering the two strategies for how to vote, superdelegates must vote in a way that disregards the benefit of supporting one candidate over another personally and rather vote as if they had no idea what the consequences would be. The likelihood of Rawls’ philosophy being on the agenda when the delegates meet in August is low. More realistic, both campaigns will scramble to make their case to the public and to the delegates the costs and benefits of each strategy. I predict that as the values of the moves in the game change with daily polls and primary wins, eventually a Nash equilibrium will be reached where a majority of superdelegates see the wisdom in one choice over another and begin a wholesale move toward the winning candidate. It is up to the campaigns to figure out how to entice and convince the delegates that their option is a winning move.  

In this essay (http://www.gametheory.net/News/Items/027.html), Regis Ferriere discusses the application of game theory in social situations. More specifically, he goes in analyzing a report by Nowak and Sigmund, who studied evolutionary dynamics. The study by Nowak and Sigmund established a theory that predicts social cooperation based on the reputations of the subjects. First, it assumes that no direct reciprocity, meaning, no subject will return assistance when he/she is given some. There is also a personal scoring system in which each subject evaluates other subjects by observing their behavior. An image point is given to those that help; and an image point is withdrawn to those who don’t offer assistance.

The system also includes a “score cut” that each subject uses to determine if he/she should assist another subject. If the other subject is valued higher than the score cut, then he should assist him/her. If not, he/she should deflect this person. If one uses the cooperative strategy by setting the score cut to zero, everyone will receive assistance.

The system proposed by Nowak and Sigmund creates the dilemma that if a subject decides to deflect another person because that other person has a low score, he/she tarnishes his/her reputation as well. This leads to a dead-end for many people. This is interesting because in my opinion, the equilibrium would be for everyone to set the score cut to zero so that everyone will assist one another, as mentioned previously. And also, there will be no discrimination under this circumstance. However, the only setback is that people cannot judge the morality of others if their standards are that low.

A few lectures ago when we started talking about power in networks and how certain nodes can have more power than others, I was reminded about a book that forms a central part of the literature that my thesis uses.  The book in question is Albert O. Hirschman’s National Power and the Structure of Foreign Trade (1945).  I couldn’t find a version of the book online (and any would probably have dubious legality), but Cornell provides a summary of it and another similar work at:

http://falcon.arts.cornell.edu/Govt/courses/F05/685/Week%205%20-%20Hirschman%20and%20Abdelal%20and%20Kirshner%20%20memo.pdf

Hirschman examined Nazi Germany’s use of commerce during the 1930s to compel smaller states in Eastern Europe to comply with it politically. He argued that given two states A and B with some volume of trade with each other, the state for which that trade comprised a greater portion of its total trade (say B) would likely be more dependent on that trade than the other.  In B, a greater proportion of the population likely benefited from this trade and would be hurt economically if it ended. These individuals would thus pressure their government to do whatever was necessary to maintain or even expand that trade. State A would likely face similar pressures, but on a much lower level and would thus be less dependent (meaning that it had more power).  Subsequent literature’s muddied the picture a bit and added several important considerations, but the basic idea still stands.

This ties in neatly with the idea brought up in lecture that a node with fewer edges (and thus more dependent on each edge) was likely to have less power than one with many edges.  The similarities between these two could be strengthened even further if we were to give valuations for the edges – where one node values some edges more than others.  Similarly, a state that had many trading edges with very small values could probably get away politically with getting rid of one or two, but one with only a few high-value edges probably could not without serious domestic political repercussions.

I thought it would be interesting to bring this recent poll on the web to Cornell Info 204 blog

Slashdot poll gets Cognitive Dailyed gets Info 204-ed

How Many People Will Select The Same Option As You?

# 0%

# 1-25%

# 26-50%

# 51-75%

# 76-99%

# 100%

Before you click on the results at the bottom of the post to see what most people have chosen, I would like us to consider the options with our game theory hats on. Don’t look yet!

First let us consider the question itself.

“How Many People Will Select The Same Option As You?”

Although there is no payoff per se, we can treat this as a game where you win if the percentage of people who pick the same choice corresponds to the percentage range. Thus, this is essentially a coordination problem, where a group of people have to solve a problem without being able to communicate with each other. From game theory class, we may have learned about Schelling games and focal points. This game, however, has the additional property in which the choice you make not only relies on coordination but directly affects the distribution of results and hence the “correctness” of your answer. At one moment, you choice may be right, but at a later time, it may be wrong and vice versa. This also raises the question of whether you want early victories, late victories, short-term or long-term victories. Alright, let’s delve into the various choices themselves.

0%

This option will only be right if you are the one and only person choosing it. What are the odds? If you are the first person on the poll and you choose this option, you win trivially. But every subsequent person will not be able to choose this option and win. The next “rational” person might reason that the first person would have chosen this option to win on the first round. Thus he will not choose this option but rather one of the other five options. If he chooses 1-25%, he will not win until the next 3 people come and only one of them chooses the same option, giving him the 25% victory. At any rate, we can reasonably say that choosing 0% and expecting to win is a very unorthodox strategy as it relies on thinking that no one else would adopt such a strategy.

This brings us to the point of simultaneous-choice games versus turn-based games. The type of game choice mechanic can affect the chance of winning greatly. In this case, we have an ongoing choice game where it is assumed to be almost simultaneous if all the results are collected and only tabulated at the end. So 0% is a very unlikely victory choice, since the more people are polled, the higher the chance of there being people who wish to seek unorthodox 0% victories there will be.

1-25%

Since there are 6 choices, assuming an even probability of each choice would make some hasty thinkers choose this option. It is also very tempting indeed as it provides a high chance of short term and long term victories. If we assume a normal distribution we can almost safely choose this option and hope that in the long run there will be less than 25% of the people choosing this altogether. Here we come to the interesting bit where many people choose to adopt this seemingly victorious strategy and hence driving up the percentages, and ultimately resulting in defeat for the >25% who happily picked this. So this poll is not as straightforward as it might be. We will come to see as we explore the other options. (Gosh this option is unpopular again!)

26-50%

Using the same normal distribution argument, we might expect a sizable percentage of people to end up here. Rational people who rejected the previous option might also end up here as it provides a very stable long term victory option despite the fact that it might take awhile for the polls to reach the 25% required for victory.. To have >50% of a polling population choose this option would take a longer time than to have >25% of the people choose the second option. We should also note that it is perfectly possible that there is more than one winning strategy as 25% pick this option, 1 person pick the 0% option and >50% pick the 51-75% option. If the cards fall right we can have a sizable percentage of people winning despite different choices. Isn’t that just awesome.

At this point we should begin to realize that our notion of rational behavior is being challenged. There is no pure rational equilibrium strategy for this game. We should instead rely more on psychology, reasoning and intuition.

51-75%

This is quite a bad choice to pick as it has no noticeable focal properties, and 51% is a very hard target to reach, whether distribution-wise or from reasoning psychologically. I intuit that it is very unlikely that this choice would even exceed 20%. From our previous reasonings, it is better to pick the previous 2 options. We are relying on those more reasoning challenged individuals to pick this option. (Well some people reason differently after all.)

76-99%

This option is even worse than the previous. The only saving grace is that perhaps, there seems to be a good Nash-like equilibrium where if a sizable population somehow manages to end up here, it is very hard to deviate from this range. So if cooperation were somehow telepathic, we could have at least 75% of the people victorious. But I feel it unlikely. There are other more compelling options which relegate this option to a slim chance of victory. People are pretty much selfish and not all that cooperative on small or large scales.

100%

This might be considered the Nash equilibrium or most socially optimal solution to this problem where we can have 100% victory. It might also be considered a focal point of this poll. Perhaps if there were a sizable incentive, a great number of people might decide to miraculously (or rationally) cooperate and ALL choose this option. But if that is the case, some might feel that the previous option provides just as great a chance for massive cooperation since a small number of dissidents will always be present to screw up the population.

Alright go ahead and see what people picked to see if you have “won”. Here are the poll results results from the original Slashdot poll.

I would like to comment that this poll is not as trivial as it appears and its results can be applies to various fields of studies, especially in terms of the market economy, where the distribution of people’s choices has great impact on prices, profits, etc. We can also apply it to politics and society, where unanimity is rare, cooperation sporadic, and falling in with like-minded groups a considerable advantage. To sum up, game theory and analysis of networks are essential for modeling a system but oftentimes, it is more important to consider the psychology and reasoning dynamics of the people playing the game.

The investigation of networks is not only applicable to the human population, but also to animal populations. The emergence of distinct groups within populations of wild animals is used to distinguish new species. The in-class example of isolated groups of the human population not connected to any “giant component” is precisely analogous to Darwin’s studies on island animal genetics (albeit not on an evolutionary timescale). Geographic isolation accounts for three of the four modes of speciation (Allopatric, peripatric and parapatric). These rely on the effects of habitat fragmentation or bottleneck effects, and are thus easily explained by fragmentations of a network.

The fourth kind of speciation, called sympatric speciation, is where populations diverge genetically while inhabiting the same region. This rare phenomenon is speculated to be occurring within the world’s most widespread marine mammal population, that of wild orcas (Killer Whales).

In representing the animal populations as networks, what do edges represent? In the human population, we consider an edge the availability of communication. In the natural-world network of the orca population, the relationship between two nodes could be defined by similarities in behavior. Cetaceans are one of the few orders of animals to exhibit creative behaviors, which are then assimilated by offspring and other individuals.

Researchers have defined a few broad sub-components of the wild Orca Population:

• Resident populations stay in certain coastal regions and generally consume salmon. They live in large “matrillines” of several generations traveling together with a common female ancestor. Their vocalizations are population-specific and they exhibit extensive surface behavior, such as breaching and spy-hopping. Genetically they are related with similar coloration patterns and fin shapes.
• Offshore populations inhabit waters farther from the coast and also feed on fish, but congregate in large groups of 20 to 200 individuals.
• Transient killer whales have the largest geographical range, overlapping with the other two types, and have larger dorsal fins. They also are more conservative in surface behavior and feed exclusively on other mammals, such as dolphins and seals.

Scientists are unsure of what to make of these discrete components within the population. Is it simply variance in heritage and morphology, or is it evidence of the emergence of a new species? Another unanswered question is if there is reproductive isolation within each sub-population. To what degree do individual orcas interact or reproduce with other populations?

The National Marine Fisheries Service is attempting to get one population, the Southern Resident population near Puget Sound, off of the Endangered Species List. This population of only 88 individuals was discovered to be separate because of a specific diet and a range limited to coastal North America. The recognition of this discrete group is vital for targeted conservation efforts, as resident groups, compared to transient populations, are especially vulnerable to habitat loss and extinction.

For more information, visit the NOAA Fisheries site on Killer Whales.

Looking for something to write about for my Econ 204 post, I stumbled upon gametheory.net—a comprehensive site on game theory (as its name obviously suggests).  The site has information about game theory books, a dictionary of game theory terms, links to news on game theory, a section on game theory in pop culture, and, of course, games you can play to test out the theories.

When you first come to the site, there are four options: educators, students, professionals, and geeks.  As you have probably quessed, being a Cornell student, I clicked on the link for geeks.  Toward the top of the geek page it says:

“In the children’s game Memory, players alternate turning over pairs of picture tiles trying to get a match. Game theory suggests that it is not always advantageous to turn over a known pair!”

This counterintuitive fact immediately piqued my interest; something I had never bothered to doubt (I mean, come on, what kid will not turn over a known pair) was not true according to game theory.  I searched around the site to see what other interesting things I could find.  Here are some of them:

New tack wins Prisoner’s Dilemma

This article answers one of last week’s homework questions (number 4, on repeated prisoner’s dilemma).  It discusses a new variation on a highly successful tactic called tit-for-tat.  In the classical tit-for-tat, a player cooperates for the first move and then copies the other player for each consecutive move.  This strategy has been proven to produce better results, than just playing the Nash equilibrium.  Where was this when I did my homework last week?

Is the key to Survivor in ‘non-cooperative games’?

Another interesting article on the Nash equilibrium.  This one discusses the famous concept in the context of the TV show Survivor.

Game theory in film: Princess Bride

This well-known movie has a funny scene which has some game theory.  It involves bluffing and trying to figure out the other player’s strategy—albeit with an interesting twist at the end!

Large social networks - a good thing to have. It means more friends, more contacts, and more connections, simply, but researches at the Virginia Ann Arbor Health Care System and the University of Michigan in Ann Arbor have recently conducted a study that implies that a large social network may also be a health benefit. The subject of the researchers’ study were 605 hospital patients that had recently received operations in the chest and abdominal area. By carrying out massage therapy as well as asking patients about how many social connections they had (measured by number of friends and frequency of meetings with them - in other words, they measured only positive ties), the researchers concluded that there was a direct correspondence between recovery rate and size of the social network the patient was in. Not only that, but patients with many connections also required less pain medication, and were generally more relaxed pre-operation. Similar how a node connected to many other nodes has the most access to information, being part of a large social network implies more support from family and friends, therefore minimizing anxiety before a surgical procedure, as well as lessening the chances of depression after one.

The research is largely aimed at surgeons and hospital staff. For one, social networks may soon become another question to fill out when entering the hospital soon - if the conclusions of this study gains momentum, then hospitals may use the size of your social network to gauge how to best prepare you for an operation. For another, it also clues hospital staff (such as nurses) into which patients may need more continued support. Isolated patients may need to rely on staff instead, filling in the gaps that the lack of friends and family creates. In other words, when their own networks don’t suffice, there is the possibility that it would be necessary for the staff to draw the patients into their network instead. Social Networks are gaining more focused attention in a variety of areas; even employers now sometimes use online networking sites such as Facebook and MySpace to research potential job candidates. The world of medicine is yet another field in which its influence is being discovered.

The article, ‘Socially Connected People Do Better After Surgery’ was published in the February 2008 edition of Journal of the American College of Surgeons. A link to the article can be found here: http://www.sciam.com/article.cfm?id=socially-connected-people.

Why do certain songs sound so good? Why are there simple tunes that are so catchy? How can we tell immediately that some sounds just don’t go well together? Of course, there are many factors that contribute to how music is interpreted by human ears, but much can be understood by seeing the networks behind music.

In this article on combinatorial music theory, Andrew Duncan first represents the basic music scale, a 12-tone, equally-tempered scale as a graph. Each of the 12 nodes represents one of the 12 notes in an octave. The most basic graph Duncan includes is one where there are edges between adjacent notes, or notes that are one increment in pitch apart from each other. (In physics, we see that the pitch and the frequencies of wavelengths of the pitch are related, but that the increments between frequencies are linear only on a logarithmic scale.)

Duncan also discusses the appearance of a network on the fretboard of guitars and other stringed instruments. Musicians know that there are not online connections between the notes along each string (adjacent nodes), but between nodes on strings below, on certain increments, or frets. Scales played as paths on a network on the fingerboard can be shifted to any node, and be played the same, harmonically speaking.

Going back to the music note network, in a more complex graph, we would have edges that are directed and weighted. The most basic scales are the major and minor scales. Take the C major scale, for instance. This is the sequence C-D-E-F-G-A-B-C, and we can draw the edges between said nodes, so that a path is made for that major scale. Additionally, we can draw edges from C to each of the nodes in the C major scale. These are the major 2nd, major 3rd, perfect 4th, perfect 5th, major 6th, and major 7th intervals, which define the weights for each edge. Furthermore, the relationships between notes are not reciprocated symmetrically. Take the connection C-E, for example. This is a major 3rd in the C major scale, but E-C would be an interval on a different scale, a minor 6th on the E minor scale. So edge C-E is weighted differently than E-C. Duncan creates separate graphs that represent each of these intervals, to demonstrate the symmetries in music.

The human ear is more attracted to certain intervals in music. For example, the beginning interval in the wedding march song is a perfect 4th. Chords, also, are more pleasant in sound. The three-note NBC tune is in fact the three notes of a major chord, the 1st, 3rd, and 5th, with the order simply switched. The intro to The Postal Service’s song, “Natural Anthem” is the minor 3rd drawn out and repeated multiple times. We can give greater weights to these intervals than the weights of, for example, the intervals C-C# or C-F# (the tritone). Played simultaneously, these intervals are dissonance to our ears.

We can think of songs, or at least melodies, as paths between nodes on a new graph. Edges are more likely to be formed between nodes with strong ties, that is, notes with intervals with greater weights. Each node, in a way, has a valuation for each other node in the network’s graph, as each note will tend toward certain other notes in music. Because of this, we find many songs that sound similar. (A teacher once said that Green Day songs are all the same progressions, simply in different keys, which, of course, does not lessen their values any…)

Finally, for the entertainment of the readers (and myself earlier), here is another link. In this online program called Graph Theory, Jason Freeman creates a graph of 61 small scores played on the cello. Each node on this graph represents a small segment of notes played on the cello. These are connected, forming edges, to other nodes with which they are compatible. The user starts with one node, and can select a node to which it has an edge, and so on, creating a simple interlude on the cello. The mini composition can then be played back. And here, we have it— music, a song created through paths on a network.

In the October 5th, 2007 issue of the journal Science, Keith Jensen, Josep Call, and Michael Tomasello published an article entitled “Chimpanzees are Rational Maximizers in an Ultimatum Game.” This article can be found here: http://www.sciencemag.org/cgi/content/full/318/5847/107

The authors study the ultimatum game and contrast human behavior with chimpanzee behavior. The ultimatum game is played between two individuals. One is the “proposer,” who is offered a sum of money and can decide how to divide it between himself and the “responder.” The responder can decide whether to accept or to decline the proposer’s offer. If the responder accepts the offer, the players receive the proposer’s division. Else if the responder rejects it, both do not get anything. Using the theories we learned in class, we would assume that the proposer would propose an unequal split. For example, if $100 were at stake, the proposer would keep $99 and offer $1 to the receiver. The dominant strategy of the receiver would be to accept whatever offer the proposer gives him—because the alternative would be to receive nothing at all. As we learned in class, the proposer holds the most “power” in this relationship and should get a majority of the value.

However, the article mentions various studies that have shown that proposers tend to make offers of 40 to 50% of the value, and responders will reject offers if they are less than 20%. This implies that responders realize when an offer is unfair and will punish the proposer for the unfair offers. Proposers who understand this will equalize their proposals.

Currently, chimpanzees are the closest relatives to humans and display some types of coordinated or altruistic behaviors (coordinated food gathering, for example). The authors decided to test the ultimatum game on chimpanzees because they wanted to assess whether chimpanzees were similar to humans in their understanding of fairness. In a modified version of the ultimatum game, the scientists confirmed that humans tended to reject unfair offers. Chimpanzee responders, on the other hand, would rarely reject any offer. Unlike humans, the chimpanzees did not even appear to be angry (i.e., throwing tantrums) when they were faced with unfair offers.

From this, the authors conclude that chimpanzees are not sensitive to the concept of fairness. In this ultimatum game, it seems that chimpanzees—not humans—are the ones who may behave “rationally” according to the economic theories of maximizing payoffs that we are currently studying.