Before taking this class, everyone had a background in game theory, whether or not he or she realized it. It had a place in our history books, as they chronicled a half-century conflict between the United States and the Soviet Union– the Cold War. The Cold War is a genuine prisoner’s dilemma, where both sides feared to engage in disarmament given the possibility of destruction. It was, as a result, of particular interest to early game theorists who collaborated with governmental agencies: namely the CIA. Although disarmament was clearly the optimal solution, it could never be realized because of a lack of cooperation. Hence, the result was a full blown arms race, costing each government billions of dollars (much like two prisoners being handed a lengthy jail sentence for confessing in the standard prisoner’s dilemma example).

The Stanford Encyclopedia of Philosophy describes the Cold War as a pair of reciprocal strategies– if one side launched an attack, the other threatened to respond with a counter-strike. Both the USA and USSR ultimately recognized the other’s incentive to attack first and implemented their best response. Consequently, the Cold War’s only Nash Equilibrium, the inevitable result, was a race to be the first to attack (or, rather, a race to be prepared to attack).

While the Cold War ended almost two decades ago, a similar game is being played today with identical outcomes. Recently, Russian President Vladimir Putin outlined a plan to research new high-tech weapons and fully upgrade the nation’s defence system by 2020. “It is already clear that a new arms race is unfolding in the world,” Putin recently mentioned to government, military, and business leaders. “Over the next few years,” he continued, “Russia will start production of new types of weapons which are in no way inferior to what other states have” (TVNZ).

The modern arms race appears to be merely another round of the preceding prisoner’s dilemma, undoubtedly bound for the same equilibrium of wasteful military spending. Although this is clearly an oversimplification of the Cold War– it was in fact a series of complex games intertwined with one another– we can be sure that in this new game will follow the same path as before, leading to the precisely the same outcome.

While all sports naturally have complex strategy to determine the victor, soccer specifically has a situation in which the game theory behind it is comparatively very easy to analyze, penalty kicks. These penalty shots are a one on one game, shooter against goal keeper; the shooter trying to guess which side the goalkeeper will not defend, and the goalkeeper trying to guess the side the shooter will shoot. Another nice simplicity of this game is that it occurs simultaneously; the ball only takes .2-.3 seconds from the kick to reach the net, so if the goalie were to make a decision after the kick it would be too late.

As a result this game can be represented by a simple 3 X 3 matrix of scoring percentage for the left, center, and right sides. A kicker’s shot depends on his dominant foot and the side opposite of that foot is his strongest shot. This side has an increased percent of scoring since it is harder to save and less likely to miss the net. Similarly goalies may have a dominant side for which they are better at saving goals (independent on a kicker’s dominant side) however this is almost insignificant compared to the shooters dominant side. Another key point to the game is that all professional goalies know of the shooters dominant foot and previous penalty shot experience (and thus is able to create the shot percent matrix).

So while each shooter has a strongly dominant side that is more likely to score than the other, he still has no dominant strategy of only shooting to that side since the goalie would then just always jump that way also. We know in theory there should exists some mixed strategy for both the goalie and the shooter such that the probability of scoring is the same at each of the three sides. The question however is do kickers and goalies follow this strategy in order to maximize their outcome. To test this data from the French and Italian first-leagues was analyzed by A. Chappori, S. Levitt, and T. Groseclose in Testing Mixed-Strategy Equilibria When Players Are Heterogeneous: The Case of Penalty Kicks in Soccer, and were condensed in the tables below.

TABLE 3—OBSERVED MATRIX OF SHOTS TAKEN

|                                                  Kicker

|                              Left    Middle    Right    Total

|              Left           117      48          95        260

|Goalie  Middle           4         3            4          11

|              Right          85       28          75         188

|              Total          206     79         174        459

TABLE 4—OBSERVED MATRIX OF OUTCOMES:

PERCENTAGE OF SHOTS IN WHICH A GOAL IS SCORED

|                                                 Kicker

|                                Left    Middle    Right    Total

|               Left            63.2   81.2       89.5      76.2

|Goalie    Middle          100     0           100       72.7

|               Right          94.1   89.3        44.0     74.4

|               Total          76.7    81.0        70.1    74.9

“Notes: The sample includes all French first-league penalty kicks from 1997–1999 and all Italian first-league kicks (1997–2000). For shots involving left-footed kickers, the directions have been reversed so that shooting left corresponds to the “natural” side for all kickers.”

According to the data kickers shooting to the left have a 76.7 % chance of scoring, middle 81%, and right 70.1% with a average of 74.9%; goalies defending left have a 23.8% of saving, middle 27.3% and right 25.6% with a average of 25.1%. Based on these numbers the percentages are quite similar, close enough to be within statistical margin of error. We therefore can conclude that both shooters and goalies in penalty shots use mixed strategies to maximize their chance at a goal and a save respectively. So next time you watch a penalty shot understand there is a lot more than physical strength speed and skill, these players also have to be experts in mixed strategies and the numbers behind it.

After a long night of tossing and turning last week, I decided to pick up a magazine to lull myself to sleep. Unfortunately, the only stack in my fraternity’s bathroom was of Playboys, and the obvious thing to do with those would only serve to keep me up even longer. Then I remembered what my dad would always tell my mom - he likes the articles. So I decided to give it a go and look away from the busty cowgirl on the left and the not-so-innocent Catholic schoolgirl on the right, and focus my eyes on the article in the middle of the page [Playboy, March 2008, The Look of Love, pg. 99].

While most of the article (read: most important part of the article) dealt with how to properly pick up signals from girls, my nerdy Cornellian self became engrossed by the section which proposed a mathematical model for marriage. Specifically, the author proposed a game theory problem regarding the decision of which partner to propose marriage to. Each player (person) wants to maximize his or her payoff, which is abstracted to be the strength of his love for his spouse. In other words, each player Pi, out of the set of all people willing to marry him or her, wants to marry the one he or she likes the best out of the set. However, the circumstance is complicated by the fact that in a monogamous society personal evaluation is sequential and not parallel. In other words, in order to evaluate his affection for another person, the player has to date him or her, and he or she can only date one person at a time. This poses a problem. If the player proposes to too early a partner, he or she may not have yet met someone better. Therefore, proposing too early leads to a sub-optimal expected payoff. Likewise, a player should not propose too late, for by the time he or she decided to tie the knot, he or she may had already dated and broke up with “the one.” In this case, he or she has to settle for someone sub-optimal because his or her perfect partner is in the past. This model assumes that a person will not take back anyone that they had already dated and broken up with. The author, not going into mathematical detail or empirical methodology, cites Miller’s The Mating Mind proposing an optimal strategy dubbed “the 37 percent rule.” The strategy states that to maximize expected payoff, the player should date 37% of his expected partners, remember how much he or she liked his favorite of the bunch, and then marry the very next partner whom he loves at least as much.

Of course, not everyone has an online subscription to Playboy (I keep one around purely out of scholastic pursuits such as this, I swear!), so instead of focusing on the above model, I instead used it to springboard to another article which I found interesting. Authored by Williams, The Mathematics of Dating: Applying Game Theory to Win a Spouse [http://www.associatedcontent.com/article/465911/the_mathematics_of_dating_applying.html] deals with a more advanced model of dating and marriage. Whereas the Playboy article assumed what Williams terms “closed players” who will not date a person more than once, Williams’s model introduces another type of player - an “open player” - who is open to dating his partner again after they have dated other people. This model complicates players’ strategies even further. While breaking up with an open player carries less risk since another round of dating with him or her is possible, a player must be more sure when breaking up with a closed player.

On his path to optimal strategy, Williams proposes multiple possible strategies that at first glance seem to be optimal. Interestingly enough, positively-connoted strategies such as “Idealistic,” “Acceptance,” and “Young Love” strategies proved to be the worst. The top 3 were “Desperation,” “Stalker,” and “Nagger.” A Desperate dater will go down his or her list of favorites and propose to them in order until someone (anyone) says yes. If no one does, he or she will propose to every person he or she dates. A Stalker, on the other hand, keeps proposing to his favorite partner until he or she accepts (for example, if that person’s favorite person marries off and our Stalker is the next one on the list) or gets taken off the market (marries off). A Nagger - who proves most adept at this dating game - combines the two strategies by desperately proposing to everyone on his list in order every time he goes on a date. This way, he or she can come back to Open Players who rejected him or her (Desperate dater’s weakness), but not get stuck on one person (Stalker’s weakness).

This problem and the derived set of strategies - in particular the optimal Nagger strategy - is an interesting thought experiment and an example of applicability of game theory to everyday life. It deals both with networks and game theory. Specifically, the problem resembles perfect matching, wherein each person has a valuation (in this case his or her affection) on a product (dating partner). The difference is that in this case the edges (compatibility) don’t get drawn in until the two nodes (people) had dated. Furthermore, whenever a pair is matched (married), it gets deleted from the graph. In these ways, the graph is ever-evolving, with nodes appearing, disappearing, and edges being created all the time - complicating strategy.

In sum, if the dating game at times seems too much - nag. Go to your ex’s and propose to them in descending order of affection. And if (more accurately when) they all decline - no worries. Next time you go on a date with somebody new - simply propose to all of your ex’s and the new (boy/girl)friend all over again. Cheers.

Read the rest of this entry »

Manufacturers of consumer electronics are developing great devices with new features at an alarming rate.  Unfortunately, advances in battery technology are struggling to keep up with these new power hungry gadgets.  Streaming video, 3d graphics, and wireless data connections can all drain a device’s battery in a few short hours.  Some electrical engineers are taking action, and are trying new methods of power optimization at the chip level; one of their new tools is network theory.

A number of researchers are looking at applying principles of game theory to designing VLSI chips (very large scale integration –complex processors, etc).  Specifically, when devices get that small, signal noise becomes a major issue due to the close proximity of transistors.  Engineers have started modeling the networks of these circuits as games, trying to find the balance between logic gate size and signal noise, or propagation delay and interconnect placing, with a Nash equilibrium.  This way, less power can be lost to noise in this new, optimal flow pattern.  Some links to research in this field can be found here:

Simultaneous Interconnect Delay and Crosstalk Noise Optimization through Gate Sizing Using Game Theory

Game Theory and its Application to VLSI Physical Design

Similar research is being done at Rice University.  In a recent spotlight article in the Technology Review, Prof Krishna Palem talks about his Probabilistic CMOS.  Using a few ideas not yet covered in class, specifically Bayes rule, he is able to take advantage of conditional probabilities and have his circuits care less about values of lesser importance.   In these less important parts of the chip, the voltage is lowered, and while this increases the likelihood of error due to signal noise, the value coming from the calculation has already been deemed trivial.   Palem believes that these chips may account for a 10x increase in the battery life of many user devices. 

Probabilistic Chips  

The giant online auction company, eBay, has announced a policy change to increase the trader fee (commission) charged during a transaction between buyer and seller. Beginning in May, 2008, the company will also introduce a new feedback policy that no longer allows sellers to offer feedback of its customers. eBay reported that some sellers were retaliating against customers who gave them a bad rating, resulting in rater manipulation and sometimes extortion. Critics argue that by removing seller-feedback makes the system asymmetric and give too much power to buyers. Some sellers have organized a week-long boycott of eBay and have organized themselves on social networking sites like MySpace and YouTube.

The effect of increasing trader fees can result in reduced profits for the seller and/or increased prices to the buyer depending on the changes to the buyer-seller graph. In a closed network, a boycott of sellers would result in driving up prices to buyers by reducing competition between sellers. In reality, buyers and sellers are not confined to a single online auction site and may simply take their business elsewhere.

Dr. Hughes, a professor in the Department of Sociology at the University of CT, wrote in article in which he used the Prisoner’s Dilemma to explain Western society’s general practice of monogamy. He demonstrates the prisoner’s dilemma game and societal equilibria for three types of monogamy: patriarchal polygyny, loose patriarchal monogamy, and strict monogamy (the form of monogamy generally accepted and found throughout the US and Europe). The article can be found at: http://hackvan.com/pub/stig/life/Monogamy-as-Prisoners-Dilemma.html

Many anthropologists believe that monogamy is not actually a “natural” behavior for humans. We are one of few species to practice monogamy. Yet monogamy has been the reigning keeper of western relationships for as long as we can remember, with non-monogamous practices continuing to decline. Dr. Hughes reveals that as we see more gender equality we continue to see a decline in non-monogamy and the pay-offs for infidelity become harsher.  The US and most western societies are classified as strict monogamy societies. Under strict monogamy infidelity is likely to be reported (whether it be to a church, community, or even the law in divorce and custody cases).

Essentially, the loyal partner has more power over a partner practicing infidelity. Just as in the prisoner’s dilemma game where the confessor has more power over the non-confessor.

Hughes demonstrates the payoffs for fidelity and infidelity within a strictly monogamous society using the Prisoner’s Dilemma game where the Nash Equilibrium is (monogamy, monogamy) or (1,1):

The game uses several assumptions:

 (1) The value of a relationship can be summed up in one measure, a unitary dimension of demand.

(2) The value of a relationship is reduced if a partner is not loyal, bc of humanities general inclination towards jealousy or uncertanity. With 1 being a satisfactory whole and <1 being an unsatisfactory fraction. The relationship is not reduced to 0 because a libertine (a libertine classifying any human in western society) might recieve some satisfaction knowing that their partner’s infidelity frees them to engage in infidelity as well.

(3) The utility of a monogamous relationship is equivalent for everyone. 

(4) Sexual contracts are reciprocal and subject to the same constraints.

The majority of American couples see the risks of covert infidelity, in disease, partners’ discovery, etc. to be inferior to its benefits. Even affairs rarely continue for any length of time without resolving into monogamy with one partner or the other (Hughes, 1992). Despite some infidelity the pay off matrix is still that seen in the above figure (figure three) with mutual monogamy equal to an equilibrium.

Even the minority of people who have come to accept infidelity in their partner is trapped in monogamy by a prisoner’s dilemma. As long as they are each pursuing the best outcome for themselves… non-monogamous arrangements collapse, and society is forced to revert to monogamy.

 Huges writes that “to escape from this prisoner’s dilemma the potentially non-monogamous must organize, submit to a new set of enforced norms, and create a non-monogamous community of sufficient size to achieve closure.”  Although this has been seen in some strict mormon communities in the past, the NE of monogamy has led these communities to dissolve.

Despite species natural tendencies toward polygamy, monogamy remains a natural Nash Equilibrium for Western society and it appears likely to remain that way unless society completely reverts its relationship norms and values. Whether we are forced into fidelity through the prisoner’s dilemma or whether are values and norms created the prisoner’s dilemma in the first place, is debatable.

The modern Republican Party can essentially be divided into several factions: social conservatives, fiscal conservatives, defense conservatives, paleoconservatives and libertarians (more at Wikipedia).  While not nearly as clear-cut as examples we have seen in lecture, this sort of arrangement naturally lends itself to conceptualizing by the network model.  To understand the nodes (party subgroups) and edges (relationships among subgroups), an explanation of the different wings and the issues they hold dear is necessary.

Social Conservatives

The social conservatives tend to focus on issues of morality according to their (predominantly Protestant and Evangelical, but also Mormon, Catholic and Orthodox Jewish) religious beliefs, and support legislation proscribing certain practices (e.g. abortion, gay marriage, physician-assisted suicide). They generally have a negative view of illegal immigration, but this is certainly not universal. On matters of the economy and foreign affairs, they tend to support the official Republican platform, even while some segments of the group are aligned with paleoconservatives. The Republicans largely have Lyndon. B. Johnson and the Civil Rights Act of 1964 to thank for this reliable constituency.

Fiscal Conservatives

This faction wields a great deal of influence over the general platform of the party, probably more than any other group save the social conservatives.  Even so, liberal immigration reforms championed by this wing for the economic benefits they would result in suffered a humiliating defeat by other conservative groups.

The fiscal conservatives advocate a smaller government, and especially one that adheres to a laissez-faire economic policy. Most support the abolition of the estate tax and reductions in income, capital gains and corporate tax rates. The rather immoderate increase of the national debt during the past six years of Republican control of government has been an especially sore spot, as this debt has implications for the global flow of capital and the management of monetary policy.

Defense Conservatives

The defense conservatives lobby for a strong military, global force presence and national defense system. Most members support foreign interventions, pre-emptive and otherwise.  For occasionally backing expansions in scope of some aspects of the government and for hawkishness of military matters, they are at intermittently at odds with the libertarian conservatives. Though often referred to as neoconservatives, the neoconservatives are more a fusion of defense and fiscal conservatives. An argument could be made for the inclusion of neoconservatives as a distinct branch of the party, however, their representation among the general population is quite small compared to representation at higher levels of government and in the editorials section.

The defense conservatives frequently share a significant overlap on issues with the social conservatives, and paleoconservatives to a lesser extent (primarily on the issue of immigration).

Paleoconservatives

Probably the group most at odds with the party as a whole, the paleoconservatives argue for a noninterventionist foreign policy, strictly closed borders and a protectionist economic policy. While customarily regarded as anti-authoritarian, they are staunch campaigners for government involvement in the mandatory maintenance of what they regard as traditional (Christian) family values. Longtime standard-bearer Pat Buchanan has recurrently voiced his exasperation with the Republican Party, and has run as a third-party presidential candidate a few times.

Altogether Now

There are currently numerous digressions from the “big tent” platform of the Republican Party, such that at least a few points of contention can be seen among each camp.  Libertarians are alarmed by what they see as an erosion of civil liberties as a result of the ongoing “War on Terror.”  Fiscal conservatives are disappointed by accumulation of national debt and the immense cost of the conflicts in Iraq and Afghanistan. Religious conservatives are dismayed by the apparent lack of action on Roe vs. Wade.  Paleoconservatives, by and large, would welcome a withdrawal from Iraq and were horrified to see the leader of the Republican Party campaign for liberal (open-border, in their view) immigration reforms.

Defense conservatives are broadly the most pleased of the major branches, seeing preemptive war in Iraq and the dramatic increases in domestic security funding as positive developments. But for each of the situations they regard positively, at least one other faction has the opposite opinion.  Clearly, there is latent tension within the party, which presents an opportunity for Democrats that they have made little headway in exploiting.

The 2006 election cycle saw libertarian conservatives and some elements of the fiscal conservatives gravitate toward the Democratic Party, historically the bearers of “big government.”  Even the bedrock was not spared erosion, as small but consequential numbers of social conservatives jumped party lines and contributed to nail-biter elections of conservative Democrats in states throughout much of the country, such as Pennsylvania, Virginia and Montana.

The Future of the Party Coalition

The 2008 election cycle promises to be even more interesting.  Republicans seem all-but-certain to nominate John McCain; trades at prediction market InTrade indicate a consensus probability well over 90%. While he seems, on the whole, to have solid conservative credentials, he has at time conflicted with almost every wing of the party. He angered anti-immigration conservatives with his support for the Comprehensive Immigration Reform Act of 2007, libertarians for his coauthorship of the allegedly free-speech-resricting McCain-Feingold Act (a campaign finance reform bill), fiscal conservatives for his refusal to fully commit to no new taxes, paleoconservatives for backing free trade agreements and defense conservatives for his uncompromising positions on interrogation techniques such as waterboarding. Though he has long since lost the nomination, Mike Huckabee’s dogged and continuing presence on the political scene hints at a nascent protectionist/isolationist undercurrent taking hold in the party. This is a horrifying prospect to the upper echelons of leadership, who rely heavily on fiscal conservatives and would like to see Hispanics subsumed into the party base.

Some elements of the party will continue to be attracted to Democratic candidates, especially the libertarian and fiscal conservative wings. While media observers have suggested that a schism or collapse will take place (see here) and these blocs will caucus with Democrats, this seems unlikely in 2008 as both Democratic candidates have not been making compelling overtures to either group.

Taken together, these events hint at the possibility of a party realignment taking place in coming years, similar in scale to the appearance of Ronald Reagan’s Reagan Democrats of the 1980s or the Dixiecrat to Southern Republican transition of the 1950s and 60s, both of which contributed to Republican political dominance since 1945. For some time this network will balance, but as new issues create new divisions within and among constituencies, the network must again be rearranged.

            In lecture, not too long ago, the topic of balanced networks – namely balanced, triangular networks – was discussed. We defined a balanced network as one containing all three positive links (e.g. a three-person friendship) or one containing two negative links and one positive link (e.g. two friends who mutually dislike another). In class discussions and homework, we were urged to consider why this would be the case:

            It seems intuitive that there would be tension between three negative links, and it also seems rather intuitive that two positive links and one negative link would leave one node (person) in an awkward middle-ground. Consequently we believe that when let alone, these networks proceed toward a more balanced state.

            This idea brings me to the topic of this blog post: Mitt Romney’s public endorsement of John McCain, which can be read in length at:

http://www.cnn.com/2008/POLITICS/02/14/romney.mccain/

            Although it may seem shocking that Romney – effectively driven out of the running by McCain – would endorse McCain, I argue that this reverts back to the balanced network principle:

It has been quite common – and almost expected in recent years – in history, for a candidate who has just dropped out of the running to publicly endorse another still-in-the-running candidate. Let’s consider this from the standpoint of a triangular network, because typically a drop-out candidate only endorses another when there are at least two candidates still in contention.

            While campaigning, candidates fiercely combat one another during debates, in speeches, in commercials, etc. This, naturally, imposes a largely negative strain on the links between said candidates. For relevance’s sake, we’ll analyze the candidates above. Before Romney dropped out, Republicans were left with (essentially) only McCain, Romney, and Huckabee to decide on – and yes, Ron Paul is running as well, but we’ll just consider the top three as our triangular network.

To ensure their own livelihood, these three candidates are forced to ridicule one another’s campaigns in an attempt to gain ground on their opponents at any given opportunity, and thus we have (during Romney’s campaign) an imbalanced ( - , - , - ) network. However, we notice in the above article that shortly after dropping out of contention, Mitt Romney chose to endorse McCain. This, it seems, would provide evidence of an imbalanced network tending toward a balanced one, as we now have ( + , - , - ) – with the positive link between McCain and Romney, and poor Huckabee being ganged up on. As the article explains, Romney is very happy to endorse McCain and believes that he will be the optimal choice for President in November. All three candidates had been under immense pressure, when battling with two opponents, and consequently, Romney sought his first chance to stabilize the network. We can imagine that McCain also is relieved to have this endorsement, as he now is part of a balanced network, and can focus his own intentions – combined with the wishes of Romney - against his (effectively) sole competition – Huckabee.

Moral: What seems to perhaps be a publicity stunt, is actually a man removing himself from an imbalanced network by forming a friendship.

The Office of Population Research at Princeton University explores historic, present and future trends in population growth, decline and control, which in turn has consequences for network structure and interaction, economic viability, social mobility, governmental regulation and environmental capacity. One of the most famous experiments conducted in this field is the Princeton European Fertility Project, which “create[d] a quantitative record of the European fertility transition” and “determine[d] the social and economic circumstances that prevailed when the modern decline in fertility began in the hope of elucidating the causal mechanisms of the fertility transition.” This was conducted by collecting demographic data from 1,229 provinces all over Europe for the last two centuries and correlating socioeconomic outlooks of the time.

One of the most obvious reasons as to why population study is relevant to “Networks” is that each node generally depicts an individual within a larger context, which is the overall population. On the macro-level, the actual size of the network grows and declines based on the motives and decisions of that particular node at the micro-level (Schelling). This can be applied towards population in the question of whether or not to reproduce due to the cost-benefits outlays of rearing another child. Are there sufficient fruits for the labor involved? In fact, this has a direct game theory application in terms of choices and payoffs. For example, compare the costs of tuition at Cornell for parents if they rear another child versus splurging that money towards some R and R instead.

Or in the case of Princeton European Fertility Project’s focus on the 19th and 20th centuries’ population transition, how the payoffs for families to invest their eggs in half as many baskets became more advantageous. This period of population transition, when high birth and death rates moved towards low birth and death rates, with an underlying period of higher birth than death rates, resulted in large short-term population growth. The carrying capacity safety valve was released by migration to North America, opening up more “fixed” resources like land and offsetting otherwise finite constraints on the network.

More interestingly, however, is the implication of how birth rates ultimately caught up with death rates during population transitions. As shown in the second diagram below, there is generally a threshold after 10% of the population decreases their fertility rate which can be described as a ‘tipping point’ that catches on like wildfire to the rest of the population (Fahey, Gladwell). In line with Lesthaeghe and Wilson’s conclusions in 1968 to the Princeton European Fertility Project, Cornell Natural Resources Professor Tim Fahey attributes the cause of the ‘tipping point’ to a small component of secularized “free women” who broke traditional social norms and codes about fertility, creating a new smaller family size social convention that diffused rapidly to the rest of the population. Nevertheless, this has yet to be seen in places like sub-Saharan Africa, where the fertility rate remains consistently above 6.

http://www.reuters.com/article/pressRelease/idUS128592+05-Dec-2007+BW20071205

http://www.csoresearch.com/news/articles/release_120507.pdf

The article linked above details an alliance formed between MonsterTrak and Career Services Offices, two powerful online career service providers. MonsterTrak has become widely adopted, however CSO still remains the industry leader in career services automation. The two companies will now be able to offer an improved product to their clients. Their pairing will allow MonsterTrak’s innovative student oriented model to combine with CSO’s first-rate software. By working together, these online service providers will expand in an already large community.

In this instance, MonsterTrak and CSO form an edge that represents a local bridge in the network. MonsterTrak’s job recruiters now have access to more college students through the career services that use CSO and vice versa. The recruiter node would have a difficult time connecting with a student that uses CSO if this newly-formed local bridge did not exist. The bridge provides the endpoints with access to hard-to-reach parts of the network. It has simplified the process and made job searching more efficient to both students and employees.