In the fifth millennia BCE, Western civilization began to take shape on the fertile banks of the Tigris and Euphrates Rivers. The rich soils of Mesopotamia provided strong incentive for humans to create large, organized settlements, subsisting on the power of agriculture. Eventually, these agricultural settlements became what most scholars recognize as the first Western civilization. But, how and why did these isolated farming communities intertwine themselves to create ancient Sumer? While many theories exist, there is one explanation that is particularly powerful and relevant to this course: networks. “Trade and power in the fifth and fourth millennia BC” provides archaeological research showing the importance of trade networks in the development of Mesopotamian civilization.

While Mesopotamia’s fertile soil provided an ideal setting for agriculture, the land lacked important natural resources. The plain upon which Sumer existed had little or no metal, timber, and precious stones. In an ideal world of peaceful farming, these lacks would not have been devastating. But, due to the raiders of the surrounding highlands, Sumer needed protection. For this reason, trade played a critical role in the development of the structure of Sumer.

To gain better access to these resources, cities built their own trading outposts, established at critical nodes in the transportation network of goods. Cities that built the most new useful nodes and links in the trade network grew in power. A particularly important example of a powerful city establishing trading colonies is Uruk. Archaeological evidence of many settlements seemingly built for the storage and protection of goods show the breadth of the Uruk trading network. The excavations of Habuba Süd, Jebel Aruda, and other sites, classified as settlements related to Uruk, have shown the expansion of Uruk into Syria and Anatolia, driven by the new trading colonies. Through the creation of new links and nodes on the trading network, Uruk grew immensely powerful.

The work we have done in class on network exchange theory demonstrates why creating more trading colonies would lead to an increase in power. By having more potential sellers competing for their trade, Uruk could gain more favorable deals. This gave them more critical resources at better prices, fueling their social, political, and economic power. Though network exchange theory is a relatively new field, the expansion of Uruk shows that advantageous positioning in a trading network could yield great social power, as far back as the fifth millennia BCE.

Here is the original article:

“Trade and power in the fifth and fourth millennia BC: new evidence from northern Mesopotamia”

Joan Oates

http://www.jstor.org/view/00438243/ap000074/00a00070/0

How did we go from a strong housing market and the low interest rates to $200 billion total loss in financial institutions? Why is it that “bubbles” repeatedly form in the economy and inevitably burst?

Image taken from CagleCartoons.com 

Whether the system you are looking at is a financial network of banks or an ecosystem of organisms, there are similarities within network structure that can be used to predict a large disruption which moves the system from one state to another. In the recently published article “Ecology for Bankers” (directions for accessing full text below) researchers analogize financial systems to ecosystems. Because of certain feedback mechanisms and underlying linkages within a system, changes arise from the activity of a select few. This can even be seen even in such issues as global climate change, electrical systems or the Internet. The authors point out that there is a relatively small amount of study on systemic risk (risk of stock market crash) versus conventional risk (risk of day to day trades) even though the consequences of systemic risk overwhelmingly outweigh any conventional risk. Looking at the network structure of ecosystems, the authors found ‘large’ nodes that had a disproportionately large number of connections with ‘small nodes’. The small nodes similarly had few connections with large nodes. Network robustness has often been attributed to the degree in which a system can be broken down into discrete systems – or modularity. This modularity was seen in the ecosystem, though sometimes it is a tradeoff between local and systemic risk. In a network in which there are strong connections between all nodes, it is near impossible to stop a disruption such as an epidemic or a forest fire. In a network which there is too much separation, especially in the financial system, it could lead to fragmentation and also increase systemic risk.

Figure 1. Graph of the $1.2 trillion dollars in day to day transactions between thousands of banks.

The authors analyzed the topology of interbank payments using a settlement system run by the Federal Reserve System. Gathering data from 9500 banks and 700,000 transfers, the edges between the nodes were classified as strong if there were many transfers. Surprisingly, 75% of all the payment flows go through only 0.1% of the nodes and 0.3% of the edges. Again, large banks were connected disproportionately to the small banks. This would signal that there is large stability in the system because it shows modularity. The researchers pointed out that there is also the factor of ‘contagion dynamics’ in which people’s perceptions affect the system such as the overvaluation of internet stocks and the onset of panic behavior. ‘Contagion dynamics’ of public perceptions and asset valuation are an overlooked part in researching systemic risk and may be tied into the underlying risk in the network structure.

Figure 2. The core of the Figure 1 in which 75% of the value of transfers happens between 66 banks with 25 banks being completely connected. Both miniscule percentages when compared to the total number of institutions.

This research relates directly to the concepts of network structure that we covered earlier in the class. However it brings a new meaning to Granovetter’s strength of weak ties. While weak ties are not only useful in getting jobs, they are also important in the stabilization networks from catastrophic changes. Strong ties, while they may alleviate local risk, often are the cause of widespread systemic risk. The weak ties that form are often the local bridges between smaller modular networks within a larger one. Again, it is this modularity that builds a robust system. It is interesting to consider the large effect of public perception which has yet to be studied in depth. The paper was not clear in how this ‘contagion dynamic’ can be extrapolated onto other applications such as ecosystems. Author Malcolm Gladwell describes in The Tipping Point drastic changes in a different light focusing on both positive and negative tipping points. He attributes social epidemics as facilitated by the Law of the Few and the Stickiness Factor (which together create several tightly connected large nodes), and the Power of Context (which ties in unpredictable environmental effects). I believe more of this topic will be covered in class once we go into Information Cascades, Network Effects and the Diffusion of Innovations. More research definitely needs to be done with systemic risk range because of the drastic consequences from the environment to the stock market. Whether it is the next housing market credit crunch, collapse of aquatic ecosystems due to overfishing, or California sinking due to global warming, we often hold a false sense of security when we view stability. In the future, we can use network structure to identify the characteristics and predict early instability and correct for it before we reach a tipping point.

Sources

Complex Systems: Ecology for Bankers

Robert M. May, Simon A. Levin and George Sugihara

Nature Vol 451|21 February 2008

http://www.nature.com/nature/journal/v451/n7181/full/451893a.html (abstract)

To access the Full Text as a Cornell affiliated student or faculty

1. http://erms.library.cornell.edu/search/tnature/tnature/1%2C30%2C32%2CB/frameset&FF=tnature&1%2C1%2C

2. Click “Nature Journals Online”

3. Log in using NetID and Password

4. Search for “Ecology for Bankers”

http://www.foxbusiness.com/markets/industries/government/article/games-played-vote_482985_18.html

This Fox Business article discusses how game theoretic strategies might be applied to voting for a president. In particular, it cites Wisconsin as being a state where voters are allowed to vote for any of the candidates in the primaries, regardless of party affiliation. The article points out that this means a Republican can choose to vote for the Democratic candidate he or she deems to be less of a threat in the ultimate presidential election. Since this can essentially be treated as a multi-step game, it may indeed be more beneficial to not vote for one’s favorite candidate in the hopes of providing less competition in the next stage of voting. This illustrates the complexities of playing a multi-stage game compared to the one-shot game examples shown in class, as the greatest payoff may arise from having different strategies at the different rounds.

The article proceeds to describe an example where a similar scenario was attempted in the past. Lincoln deduced that in the election of 1856, if Buchanan failed to win Illinois in the presidential election, then no candidate would have enough electoral votes to win, in which case the matter would be brought to the House of Representatives. Lincoln persuaded supporters of Fillmore to vote for his favorite candidate Fremont in order to join forces against Buchanan in Illinois, explaining that it would be the only chance of Fillmore’s success. Assuming Lincoln’s deductions were correct and not simply a means of trying to steal votes for his favorite candidate, this illustrates that attempting to locally maximize your own payoff (by voting for your favorite choice) may not be the best way to get the desired outcome. This is somewhat analogous to the Prisoner’s Dilemma, in which following your dominant strategy (i.e. confess) may lead to a worse payoff than some other possible outcome (i.e. no one confesses), but the better outcome would require collaboration to effectively work.

Thus it is not always the case in a multi-stage voting scheme to vote for your favorite candidate at each round, demonstrating some possibly counter-intuitive intricacies of a multi-stage game.

In chapter 2 of the book we discussed the importance of weak ties. In Particular, we talked about Granovetter’s findings based on the interviews he conducted. From these discussions we then concluded that weak ties in networks are more powerful than we may think at first. A question that came to my mind after this discussion was: are weak ties always as powerful as they were for the people that Granovetter interviewed, or are they only important and powerful in some networks and not in others? In other words, is the power of weak ties a property of a network or can the context of the network change their strength?

I found a paper titled “Complex Contagions and the Weakness of Long Ties” by Michael Macy from the department of sociology at Cornell. The paper can be found in Dr. Macy’s website: http://www.people.cornell.edu/pages/mwm14/. In this paper, the authors argue than the strength of weak ties depends on what it is going to be diffused in the network. In the case of Granovetter’s jobs network, what was to be diffused was information about jobs. The reason why weak ties are so powerful in this type of network is that distant acquaintances presumably belong to a social circle different from yours. So they can provide you with information that no one else in your social circle has. This logic seems pretty reasonable as long as what is being diffused in the network is something like information. But what if it’s something else? For instance, what if we’re talking about a network in which a rumor is being diffused and we are trying to find out not what nodes have heard of the rumor, but what nodes actually believe it? Then it is probably not enough that some distant acquaintance tells a node about the rumor for the node to believe it. Before a persons starts believing a rumor she probably will hear about it multiple times. In this case, it is easy to see that the weak ties are no longer as powerful. If a person hears a rumor from an acquaintance she barely knows, and never hears about it again from her close friends it is very likely that she will forget about the rumor and never believe it. The same logic that lead us to believe that an acquaintance has access to information that no one else in a person’s social circle has, now tells us that the person will not hear the rumor from a close friend and therefore you won’t believe it. The same logic that made weak ties seem so powerful in one context makes them seem very weak in another context. In the paper, a contagion such as a rumor is referred to as a complex contagion: a behavior in which the willingness to participate may require independent affirmation or reinforcement from multiple sources. A contagion like information, or a virus is referred to as a simple contagion. The paper argues that the strength of weak ties is clear in the case of simple contagions but in the case of complex contagions they are not always as powerful.

It was very satisfying to read this paper because it answered the question I originally had. It also provided a more technical approach to justify their claims which was also very nice to see.

Based on this paper, the answer to my question is that the strength of weak ties is not a property that is present in all networks. It depends on what the network is describing. It becomes clear that it is important to be careful when trying to generalize a concept that was found by experiment to a more abstract setting. It can be easy to make serious mistakes by making models which ignore important details on how people behave.

In his paper, “Social Networks, Civil Society, and the Prospects for Consolidating Russia’s Democratic Transition” (2001), James Gibson uses the concept of social networks to explain how strong and weak ties between individuals can facilitate the democratization process in Russia.

The literature on civil society suggests that democracy requires high levels of public association between individuals outside of government and the family. High levels of public association are though of as good for democracy because they facilitate discourse and get people involved in governing themselves on a smaller scale. Gibson’s paper moves away from the convention of looking at associations and instead looks at social networks. His rational is that under a totalitarian state like the former Soviet Union, formal organization were systematically discouraged and suppressed for fear that they may challenge state authority. Graphically, state policy was aimed at severing the edges connecting nodes. This policy succeeded in ended formal organizations but it created an extensive informal social network. The networks in Russia had to be extensive because the population did not trust the state’s media so they turned to their friends and neighbors for any news and information which was passed by word of mouth. The more edges that could be formed between different nodes, the more exposure each node received to information.

The democratizing potential of this network comes in two forms. Gibson proposes that the extensive social network could act as a foundation for the formal organizations which encourage a democratic ethos. More importantly, in a social environment where democracy is still foreign, communities rely on the individuals who are embedded in the network for: the dispersal of new information; the promotion of democratic values; and for familiarity with the new processes. Gibson’s article is a great way of seeing how you can apply the concepts of social networks and the structure of social networks to political science.

In class we learned that a network can be composed of both “strong” and “weak” ties. Gibson argues that “strong” ties are harmful to civil society because individuals connected by “strong” ties tend to have high levels of cooperation with in the group but do not engage with groups outside of their network. “Weak” ties have the strongest impact on civil society because they foster communication between different groups encouraging cooperation on a much greater scale. Gibson fails to mention the strong triadic closure property we learned about in class, which states that if an individual is connected to any two friends by a strong tie, then there must exist at least a weak tie between his friends. The strong triadic closure property would help to better explain how the Russia’s social network expanded over time. This raises the question, while strong triadic closure can be met by a “weak” tie, there always exists a possibility that strong triadic closure will result in the formation of “strong” ties. If so, would a network consisting of strong ties be harmful to Gibson’s theory of democratization via social networks? We may also ask, what happens to Gibson’s model when we add the concept of network stability?

http://www.slate.com/id/2146867/

The article above is from August 2006 and discusses the conflict between Israel and Hezbollah. The subheading, “Can game theory solve the Israel-Lebanon war?” sounds hopeful, but the article downplays game theory’s ability to analyze political situations. It discusses prisoner’s dilemma, which it describes as an oversimplified model that is “too seductive.” One reason is that Prisoner’s Dilemma is a two-player game, and political and social arrangements involve third parties.

One interesting topic that this article discusses is Prisoner’s Dilemma as an iterated game. It mentions that game theorists have known that players may use cooperative strategies if the game is repeated. Many people believe that cooperative strategies work because of “tit for tat,” where a prisoner who confesses is punished in the next round. The article calls “tit for tat” a “poster child” that does not accurately describe real situations. It also does not describe the conflict between Israel and Hezbollah because there are multiple players and asymmetry between the players.

I do agree with the article that “tit for tat” oversimplifies real situations, but I do think that “tit for tat” explains why cooperative strategies can occur in repeated games of prisoner’s dilemma. In a repeated game of prisoner’s dilemma, if either player decides to confess, the other will respond by confessing. This ensures that neither player confesses so that over long periods of time, both players’ payoffs are maximized. In a conflict between two groups or countries, it is probably hard to apply “tit for tat” because cooperative strategies do not always produce the result that one country wants. However, “tit for tat” does show how an offensive strategy like confessing or military attacks might cause the other player to adopt the same strategy. The result is chaos because neither side trusts the other to cooperate.

Social Games and Strategies for Winning

We have learnt much about Network Exchange Theory in class and it’s significance in determining the actual and perceived balance of powers within a network by virtue of the node positions. Network Exchange Theory clearly elucidates that a situation of an individual spanning structural holes and having more opportunities for interaction (satiation) confers upon him more power within the network to achieve better payoffs and the likes.

Survivor takes a twist of the common divide-a-dollar social experiment and instead forces people within networks to eliminate nodes systematically till there are 2 final nodes (the final contestants). There are actually many implications of Network Exchange Theory as well as strength of weak ties that educate a contestant on their most effective strategy in a particular situation that would help them improve their probability of reaching the Final 2.

Kevin Drum lightly mentions this idea in his article and goes on to suggest that being in a position of gatekeeper within a network is much more powerful than one of being in a central position of a close network. In substantiating his argument, Kevin comments that Rob Cesternino played this game where “He was always at pains to keep his options open; he maintained friendly relations with as large a group as possible (and was rather good at convincing others that he had their best interests at heart, even when he didn’t). He then chopped and changed his strategy as circumstances demanded. When he needed to zig, he zigged, and when he needed to zag, he zagged. He didn’t seek to lead alliances, but instead made himself into the pivotal player, who could move from one alliance to the next, and thus swing the vote in one direction or another. By so doing, he shaped the strategic context which everyone else had to play in.”

See: Article

Indeed, a general strategy of being the gatekeeper is effective because being the gatekeeper confers options to control information that flows from both networks, and also gives one the flexibility to switch strategies and perhaps even change sides when necessary in order to maintain one’s power.

Let us examine how a position of a gatekeeper can actually be beneficial in the game. Consider the following network within a tribe.

Assume you are Player M. The tribe is split into two alliances of Y-M-E-N and O-A-J-P, with C currently being an intermediary that both alliances are attempting to woo to achieve a majority. In terms of Social Network Theory jargon, A and E represent central nodes within their respective alliances whereas C, and to a certain extent M, represent semi-gatekeepers.

What can M do at this juncture?

Knowing the idea of the power of the gatekeeper, M should realize that the power is largely diluted with having two pseudo-gatekeepers spanning the two alliances. To consolidate her power, M’s best option would actually be to remove the other offending ‘threatening’ gatekeeper and increase her power in the network.

Let’s assume things do not go as M plans and C sides with O-A-J-P, evicting Y. Now the graph looks like this: (We assume betrayal leads to severing of ties as well.)

Now an interesting scenario occurs. M-E-N are in a distinctly disadvantaged situation and A becomes the power player within the network.

What can M do?

M still has certain power owing to her virtue of being a gatekeeper to E and N, and having flexible access into the main alliance through both P and A. M’s best strategy would actually be to go for jugular and evict A by courting for the vote of P (in a sense offering a better offer to P, arguing to P that evicting A, the perceived power player confers power onto P).

Of course, the fun and frustration of such flexible social games such as Survivor is that there are so many parameters and other factors to play with. However, entering the game with a clear idea of Networks Theory and the power in networks surely is an advantage. Hence, an advice for future successful survivor applications: bring your ECON 204 textbook as you luxury item.

 paper link

http://www.jstor.org/view/00018392/di015549/01p0039q/1?frame=noframe&userID=80fde168@cornell.edu/01c0a8347300501bed2f9&dpi=3&config=jstor

As we know, there are certain people play as bridges between social networks. These kind of people can build weak ties between networks, thus can sometimes have more opportunity, like job interviews, and information. What characteristics do these people uniquely have? How much do other people in the networks care about them? What influence would have if they leave the networks? How well would they perform at work? This paper gives you the answer. This paper used a research to represent a theory(self-monitoring theory)-driven examination of how personality relates to social structure and how social structure and personality combine to predict work performance. This paper doesn’t focus on “the overall structure of network ties”, but referencing self-monitoring theory to enrich the understanding of vital network topics as how is likely to bridge structural holes and connection between structural position and work performance.

  Psychologically,  self-monitoring can be defined as the tendency for people to monitor their behavior in such a way that it fits the demands of the current situation. Low self-monitoring people tend to behave in accord with their internal inclinations, regardless of situations; while high self-monitoring people tend to behave in an opposite way.

 As concluded from this paper, personality affects the way individuals build networks: high self-monitors tended to occupy central positions in social networks; personality affects the way individuals build friendship networks over time: high self-monitors became more central the longer they stayed in the organization; self-monitoring and centrality in social networks independently predict individuals’ workplace performance. It appears that high and low self-monitors pursue different network strategies, with high self-monitors tending to occupy positions that span social divides, whereas low self-monitors remain tied to more homogeneous social worlds.

 This paper explored three models, a mediation model, an interaction model and an additive model, to find combined structural position and self-monitoring would affect individual performance.   In mediation model, the success of high self-monitors in outperforming low self-monitors is doe to the greater success of the high self-monitors in occupying strategically advantageous positions in social networks in organizations. In interaction model, prediction is that relationship between network position and performance depends on the self-monitoring orientation of the person occupying the network position: high. Self-monitors should be able to exploit high-betweenness positions more effectively. But actually can’t find any support. Finally, according to additive model, self-monitoring and structural position should independently predict performance in organizations. Results show that high-monitors tended to outperform low self-monitors, and those occupying high-betweenness centrality positions tended to outperform those occupying low-betweenness centrality positions. The overall results suggest a complex relationship among self-monitoring, structural position and performance. High self-monitors tended to achieve higher performance, as did individuals who occupied high-betweenness centrality positions in friendship and in networks. 

This point is an interesting one. It gives us a hint of the hynamic status of a network. I try to find more, like how would a network develop without a bridge to the outside; will more or fewer people in a network tend to become “bridges” ;do a network like more or less of the “bridges” people to regular people? This paper doestn’t give the results, but at least, it gives a hint to think about it.

The Monty Hall paradox is a famous problem in the field of game theory and probability for which the best strategy of the player is counter intuitive. The problem statement is as follows:

You are on a game show and in front of you are three doors. You know that there are goats behind two of the doors and there is a new car behind the third door (the assumption is that you would prefer the car over a goat). You are asked to pick a door and you will win whatever is behind it. After you pick your door, the host, who knows how the prizes are positioned, will always open one of the doors that you did not pick to reveal one of the goats. He then offers you a choice to either keep your current door or to switch to the remaining door that is unopened. What do you do?

If this is your first time hearing this problem, you might convince yourself that it does not matter whether a switch is made. Clearly, there is 1/3 probability that I pick the door with the car behind it. After the host opens a door with a goat behind it, there are only two doors left unopened. Since we have no further information about the two unopened doors, it follows that the probability of the door I picked having a car behind it has been conditioned to 1/2. Thus it would not make a difference if I switched doors.

However, the best strategy is actually to switch doors when given the opportunity. The formal derivation of this solution involves the application of probability theory which you can read about at http://en.wikipedia.org/wiki/Monty_Hall_problem#Bayes.27_theorem if you are interested. However, we can simply demonstrate by exhaustion that switching doors is indeed the best strategy to follow.

G = goat, C = car

|C|G|G|

|1|2|3|

Assume that the positioning of the prizes is as shown above (the numbers on the doors do not matter so this case is equivalent to any other starting position if we just change the door numbers) and lets say that you always switch doors when given the opportunity. Then the possible outcomes of the game are as follows.

pick door 1 and then switch = win goat

pick door 2 and then switch = win car

pick door 3 and then switch = win car

Notice that the cases in which you win the car are the ones where you pick the door with the goat behind it to start out with. Clearly there is a 2/3 probability of your starting door having a goat behind it. Thus we conclude that you will win with 2/3 probability if you follow the strategy of always switching when given the opportunity.

This is the same result that you will get if you work out the formal probability theory. Thus, we have demonstrated that the best strategy is actually to always switch doors.

http://www.fox.com/fod/player.htm?show=house

House MD is the 2nd most watched drama series on the Cornell campus according to Facebook.

What makes a story good? complex characterization, intriguing philosophical concepts, witty dialogues, and of course, complicated social interactions between the characters.

House MD is known for its screenwriting excellecy. The seemingly compliated and twisted psychological games of the characters can be, in fact, modeled by game theory.

House is the king of mind games (and sarcasms). in the most recent episode, House finds out that his best friend Dr. James Wilson is dating Amber (nicknamed “Cutthroat Bitch”), one of the interns he fired. House goes all out to figure out whether Amber is dating Wilson to get the fellowship she wanted or dating Wilson because she loves him. In order to keep the nosy House from interfering with their relationship, Wilson and Amber had to play a game of whether or not to tell House about their affair. Assuming House suspected nothing, their payoff would look like the following:

AMber

Not tell tell WILSON

5,4 4,6 tell

7,7 3,5 Not tell

With Wilson’s payoff on the left and Amber’s on the right.

Wilson’s payoff will be the lowest if only Amber tells House because House will investigate his relationship with a vengeance as well as label him as a lying friend. If only Both Amber and Wilson tell house, he will be slightly better off since he is at least honest. If only Wilson tells House, House will feel important and enjoy strategizing with Wilson, and therefore Wilson’s payoff will be the highest among the cases where House knows about the relationship. Similarly for Amber, her payoff will be lowest if only Wilson tells House because House will go all out to stalk her and try to prove that she is using Wilson as well as shower her with sarcasms. If only Amber tells House, she would not be as low because at least she is honest with house, and if both of them tell House, her payoff would be even higher because there is less mystery involved. The highest payoff for both Amber and Wilson, however, exists when both of them not tell house. If Wilson does not tell House, Amber’s dominant strategy would be to keep her mouth shut; similarly, if Amber does not tell, Wilson’s dominant strategy would also be not tell. Here we have a Nash Equilibrium that intuitively makes sense: if House does not know about their affair period, then they could have the most peaceful relationship.

Assuming that House does suspect them having an affair, their payoff would look slightly different:

Amber

Not tell tell

4,3 5,6 tell Wilson

2,2 3,5 Not tell

The payoffs for both are highest when they both tell, because this way House will have less of a mystery to investigate. Their joint as well as individual payoff will be the lowest when both do not tell because House will get extremely excited, play Sherlock Holmes, and drive everyone insane. This time the Nash equilibrium occurs at both of them telling House the truth.

However, notice that if both of them tell their payoffs will be 5,6 each because House will still be interrogating both of them (Wilson’s payoff would be slightly lower than Amber’s because he has to face House at work everyday). If they keep their relationship a secret and House never finds out, their payoffs would be 7,7 (arbitrary number. The point is it would be higher than 5, 6) since they get to enjoy a real relationship. The couple decided to take a chance. They decided to try to keep their relationship a secret and hoped that House would not find out.

But House did find out. There are no games played between House and Wilson because there is nothing else for House to find out. For Amber, however, the story is a bit different. House suspects that Amber is dating Wilson to somehow get her job back.

House therefore decides to offer her a fellowship position in exchange for her leaving Wilson alone. House’s decision-making could be explained by the following payoff matrices:

Assuming that Amber is dating Wilson because she loves him,

Amber

accept reject

10, 5 11,10 offer House

5,4 15,8 Not offer

Amber’s payoff would always be higher if she rejects the fellowship offer because if she accepts the offer she would have to leave her lover. Her payoff would be slightly higher if she rejects House’s offer as oppose to not accepting the offer when House doesn’t offer because she gets style points for killing House’s smugness. For House, if he offers and Amber rejects, then he will know that his best friend is happy and hopefully he will be happy for Wilson too. If he offers and Amber accepts the offer, his theory of Amber potentially using Wilson would be confirmed and he will at least feel some satisfaction. If he does not offer the offer and Amber wants to accept the offer, House’s payoff would be lowest because Amber will stay with Wilson and she for sure does not love Wilson. If House does not offer and amber rejects, House’s payoff would be highest because Amber will stay with Wilson, and House does not have to offer her a price and negotiate with her. The equilibrium occurs, in fact, at this cell, since if Amber loves Wilson she will reject the offer whether or not House offers the internship, and House will not offer her the position since this way his payoff is maximized.

Amber

accept reject

10, 5 0, 10 offer House

-1, 13 -2, 12 Not offer

Here the game is different if we assume that Amber is playing Wilson in order to get the job. Amber only has a positive payoff if House offers the position and she accepts it. If House does not offer the position and she wishes to accept, her payoff will be very low and House’s payoff becomes high because he saves Wilson and his theory gets proven true (which is more important to him than anything else). If Amber rejects her offer, she will get a negative payoff because she does not get the job, but her payoff will be slightly higher if House actually offers a position because this way she would at least gain a LITTLE bit of self-assurance. House’s payoff when Amber rejects and he offers is lower than when Amber rejects and he does not offer because in the second case he does not need to give up some of his pompousness by offering Amber a job.

The equilibrium occurs, thus, with Amber accepting and House not offering, since Amber will always accept and House’s payoff is always higher when he does not offer.

This creates a problem for House. House does not know whether Amber is playing Wilson or seriously in love with Wilson, so it would be very difficult for him to decide whether or not to offer Amber a position. There is also the possibility that Amber might accept the position even though she is in love with Wilson, take the job, and then secretly continue her relationship with Wilson.

Instead, being the clever man he is, House merely hints the possibility of offering Amber a position, and lets Amber be the person who states her position first. House does not know whether or not Amber likes Wilson, but he does know that Amber’s dominant strategy is accept if she does not love Wilson and her dominant strategy is reject if she does love Wilson.

Thankfully, Amber and Wilson have real feelings for each other.

Yet, this brings another problem. According to the theory of triadic closure, a network of three people could only have either one positive connection or three positive connections. In the House, Wilson, Amber network, there are positive connections between Wilson and Amber and also positive connections between House and Wilson. The connection between House and Amber at the moment is most definitely not positive since he calls her “Cut-throat bitch”. If triadic close theory holds true, House will either have to become friends with Amber, or sever his friendship with Wilson. House is known for not able to interact with humans so the possibility of him forming a friendship with Amber is highly difficult, but his relationship with Wilson is so strong that many viewers on fox.com feel that it even contains homosexual undertones. Either possibility seem completely likely, or unlikely. Perhaps a premise of triadic closure theory is that the participants have to behave rationally, which is clearly a quality that House desperately lacks.