A lesson in Scalping Dalai Lama tickets

You may or may not know, but the Dalai Lama is coming to Stanford on October 14th. This is big news! Everyone wants to see him speak, the demand for tickets is so high that tickets were actually sold out 2 weeks after his visit was announced over the summer.

Now there are 3 types of tickets you should know about:

  1. Morning lecture tickets – sold for $20 to Stanford student (more to others)
  2. Afternoon lecture tickets – not being sold, but being assigned via lottery to Stanford students
  3. Conference tickets – a bundle of both the morning and afternoon lecture and a few other things – sold for $30

So to my surprise I got the following email on my dorm chat list:

On Thu, Sep 30, 2010 at 2:39 PM, John wrote:

Hey Guys,

Before I came to school, I bought two tickets to the Dalai Lama’s
Conference: Scientific Explorations of Compassion and Altruism. I
just found out that I will not be able to make it. It’s on Friday
October 15th 9am-4pm in MemAud. I bought the tickets for like $33 a
piece online, but I’m willing to go to 30. Email if you are
interested in the tickets. One or both.


This is how out email conversation then played out:

—– Original Message —–
From: “Al-Karim Lalani”
To: “John”
Sent: Thursday, September 30, 2010 9:13:23 PM
Subject: Re: [crothers-grimm-chat] Dalai Lama Conference Tickets

NO! This is a bad economic strategy. I need to give you a lesson on
bundling. You could be making money.


On Sep 30, 2010, at 9:20 PM, John wrote:

haha i’m not trying to make money. I’m just trying to get rid of
them without losing so much

—– Original Message —–
From: “Al-Karim Lalani”
To: “John”
Sent: Thursday, September 30, 2010 9:20:55 PM
Subject: Re: [crothers-grimm-chat] Dalai Lama Conference Tickets

doesn’t this give you entrance into both the morning lecture and the
rathbun lecture at 2?

On Sep 30, 2010, at 9:23 PM, John wrote:

yeah i think. I can’t make it that day

—– Original Message —–
From: “Al-Karim Lalani”
To: “John”
Sent: Thursday, September 30, 2010 9:25:19 PM
Subject: Re: [crothers-grimm-chat] Dalai Lama Conference Tickets Anyone?

send out another email being like selling the DL morning lecture
ticket (value 20 bucks) and the Harry Rathbun Lecture ticket by the DL
that day (value $20) together for a total of 38 bucks

that way you make 5 bucks.

its called bundling.

On Sep 30, 2010, at 9:30 PM, John wrote:

I like it. You’re the man

From:     John
Subject:     [crothers-grimm-chat] Selling Dalai Lama Morning and Afternoon Lecture Ticket
Date:     September 30, 2010 9:34:18 PM PDT
To:     crothers-grimm-chat@lists.stanford.edu

Hey dudes & dudettes,

I have a ticket to the Dalai Lama morning lecture (face value $20) and the Dalai Lama afternoon lecture (face value $20) on October 15th. I can’t make it, so I’m willing to sell this bad boy for $38 all together. Email if you’re interested.


From:     John
Subject:     [crothers-grimm-chat] Can’t sell the tickets separately so I’ll bring the price down to 30. Email. EOM.
Date:     September 30, 2010 10:13:35 PM PDT
To:     crothers-grimm-chat@lists.stanford.edu

From:     John
Subject:     [crothers-grimm-chat] Ticket gone :/
Date:     September 30, 2010 10:19:01 PM PDT
To:     crothers-grimm-chat@lists.stanford.edu

—– Original Message —–
From: “Al-Karim Lalani”
To: “John”
Sent: Thursday, September 30, 2010 10:33:37 PM
Subject: Re: [crothers-grimm-chat] Ticket gone :/

Its a sad day for economists.

From:     John
Subject:     Re: [crothers-grimm-chat] Ticket gone :/
Date:     September 30, 2010 10:37:41 PM PDT
To:     Al-Karim

demand for both wasn’t there. people wanted to buy just one. and I’m an engineer anyway 🙂

I was really excited when I thought John would make some money by bundling. But it broke my heart when that failed. Here are a few takeaways though:

  • The transaction costs of passing on the ticket from the morning lecture to the person who would attend the afternoon lecture were way too high for this to be feasible
  • Next time don’t bundle non-complementary goods (I guess people were choosing between one lecture and the other, ie. they were substitutes)
  • Have patience – this whole ordeal took place within an hour. I feel like someone would have bought it for a higher price had John waited a day.
  • And on second though, don’t try to rebundle a bundle. This was less of a bundling exercise and more of an advertising exercise where we tried to change a persons perception of the bundle.

China’s Currency and African Trade

Now you might have seen the news this weekend, the Chinese Central Bank has finally decided to unpeg their currency to the dollar and despite the fact that the Yuan/USD exchange rate has remained constant this morning, everyone is expecting the Yuan to appreciate. Now the news everywhere has a lot of comments on how this will effect, China, the US and the G-20. But what I haven’t seen mentioned is how this is going to affect the rest of the developing world. Well I can tell you first hand that it isn’t going to be positive.

Focusing just on Sub-Saharan Africa, China has been praised as being a major driver of growth in the region. Apart from being a major investor, China is also a large trade partner for the region. Here are some outdated stats on their trade situation:
2. China’s Engagement: the extractive sector in Africa
China-African trade: 2005 total $39.75 billion,
Export to Africa $18.68 billion, increase 35.2%; machine and electric
products $8.17 billion, hi-tech products1 $1.83 billion, totally 53.8% of the
Import from Africa $21.06 billion, increase 34.6%; extractive sector, 86.7%
Import oil: $14 billion (38,470,000 tons; 30% of imported oil $47 billion).
China-African trade: 2006 (Jan-Sept): $40.557 billion;
Export to Africa: $18.721 billion, increase 38%; Import from Africa $21.835
billion, increase 45%.

I’m going to assume trade has increased (both import and export) between China and Africa as both regions have grown.

Now here is one major detriment to sub-Saharan Africa and the rest of the region: imports from China will become more expensive.
The simple reason being that due to massive inflation in most sub-Saharan African countries (more than 5% a year), imports are often bought in dollars.
Specifically, most importers purchase ‘containers’ of durable goods from China at a specific dollar rate, and the soon to appreciated Yuan will dictate rising import costs for the rest of sub-Saharan Africa (and all other countries that purchase imports in dollars). Given the very young manufacturing industries in sub-Saharan Africa, most durable consumer goods are purchased from China and this could have some serious problems for retail shops.
With a GDP growth rate that has decreased over the last year, this could be another setback to the region this year, though the magnitude of which I’m not too sure about since the durable retail sector isn’t as large in these countries.

Ponderings on Utility

One of my favorite occurrences from this past quarter was when my Advanced Macro Prof Pete Klenow brought in his kids to class. Apart from being ridiculously cute, they also had a message to share with the class. Mrs. Klenow asked them what the purpose of Economics was and their well-rehearsed kids shouted that the purpose was “to maximize utility!”

And that brings me to the topic of this post, what is Utility really??

Now I’ve heard vague definitions such as the satisfaction an Econ (read: rational human, Econs are slightly different from Humans) received from consuming a good or service, or even more vague definitions such as utility is a proxy for happiness. Now there has been much criticism of GDP as a measure for welfare, and since GDP per capita growth is highly correlated with consumption per capita growth, I think we can safely say that consumption isn’t the sole determinant of overall welfare. In fact our Econ 52 class has at the least taught us that utility is a function of both consumption and leisure. Our prof Pete Klenow also is working on a paper (with Chad Jones who he claims is a future Nobel prize winner) on a different predictor of utility which you can check out here.

But what really determines utility? Do we care about things such as excitement vs. long-term satisfaction, so is a roller coaster ride going to add more to overall utility than working out (which is painful in the short-term but rewarding in the long-term). If we do value short-term utility more, going with the theme of ‘living in the moment’, then this would explain why we delegate all the ‘good’ stuff for later. For example, we want chocolate cake for dessert today because we’ll get back on our diet starting tomorrow. (This is also related to our behavioral tendency to discount hyperbolically, which is that we value the present a lot (and I meant A LOT) more than the future.) The question here is: does the sum of all these instances of short-term utility greater than longer lasting utility. So will a thousand pieces of chocolate cake (and the feeling of disgust the next day) outweigh the short-term pain of working out and the post-workout feeling of awesomeness? This is something most people should answer for themselves, but I think that the utility you get from being fit lasts longer, and assuming diminishing returns to both activities, the one with the longer impact should give you more overall utility.

I think along with many other people, I believe that there are several other determinants of overall utility other than consumption and leisure. Other determinants include those that allow you to maintain a certain quality of life, so for example having access to safe drinking water so that you’re not plagued with diarrhea would be nice. Other things include up to secondary school education, low infant mortality rates, high life expectancy etc.

I think one other factor that hasn’t been discussed as much includes relationships with other people. I think at the end of the day I would much rather have a best friend than a Ferrari. That’s just me though. Maybe there are diminishing returns to relationships as well, so maybe after having 4 best friends, I’d rather have a Ferrari than a 5th best friend. But its interesting how often people (myself included) prioritize current or future consumption for something that may give us more utility, ie. time to hang out with our friends and such.

Here is an interesting model that I’ve rambled about somewhere:

Now if we were to make a very simple model for relationships, lets say that utility is just a function of N, where N is the number of meaningful relationships we have. Lets assume that N has a positive utility and constant returns to scale (I honestly think that it has increasing returns to scale when N is low, for example I believe a meaningful relationship with a sibling equips us with the skills and stability to have a meaningful relationship with a friend; but for the simplicity of the model lets assume a linear relationship). Now we also have a budget constraint, and that is our time. Now it may be a very bad model to give a price for a relationship (in hours/day) since we aren’t taking into account consumption along with several other variables. But if we had a simple equation where u = F(N) such that Pn*N = Time, if we were to maximize utility we would basically try to have as many meaningful relationships as we can. But here is the problem, I was reading an article online (http://www.psychologytoday.com/blog/the-urban-scientist/200907/what-100000-people-really-think-you) which stated “A new survey shows that most people’s circle of confidants is on average about one person smaller now. And the percentage of people who say they have no one to confide in has now reached about 25%.”

Now lets assume the number of confidants we have is a good proxy measure for the number of meaningful relationships Americans have, that has decreased over time. So using this model, the math would say that the budget constraint is tighter in that most Americans just have less time. But thanks to empirical data, I know that Americans generally have more time than they did 20 years ago (this may not apply to college students). We know empirically that due to the income effect, most people nowadays have more leisure time than before, hence they have more time to form these meaningful relationships. Then why aren’t they doing so?

These are just some thoughts on utility. There is no overarching argument, but the theme of utility is sure to crop up in the future.

A Good Ismaili is a Good Economist

So during the Golden Jubilee year (2007-2008), His Highness the Aga Khan was able to travel to see many Ismailies around the world. Now if you are unfamiliar with the term Ismaili, I suggest you click here.

During his travels, he had many messages to convey to Ismailis around the world and though many of them were timeless, I found only one to be extremely pertinent to 2007-2008. This message was that of frugality. December 2007 is the official month when the US recession started which has had several global effects, many OECD countries also fared pretty badly and most developing countries saw a slow-down in their growth.

Now back to the message of economic prudence, it was very simple: if you are a consumer then you should protect yourself from a future change in your income due to the economy. And if you are a producer, cut costs so you’ll be better positioned when the economic hardships start.

Well any forward looking consumer would have followed this advice without needing to be reminded. But not everyone is a homo economicus but instead we are homo sapiens, so it may be hard for many to have known the extent or magnitude of the recession and this sort of uncertainty may have delayed people’s consumption decisions. (And some of us wouldn’t have acted so even if we did know what the future held – its okay, self control and myopia are human problems).

Now here is some economics you should know: Marginal utility of consumption decreases as you consume more. Utility is a fancy name for satisfaction, and this first statement means that if you are really thirsty on a hot day and you consume two glasses of lemonade, the second glass won’t be as satisfying as the first glass. Consumers realize this, so they smooth their consumption over their lifetime. So instead of consuming all their income when they are earning the most in their 40’s (owning the fastest cars, living a lavish life) and then consuming nothing when they are retired, rational consumers spread out their consumption over their lifetime. So they’ll buy a Volvo instead of a BMW when they are rich, and be able to take trips to Florida instead of living on the street when they are poor.

Volvo's arent that bad actually

So a good Ismaili would have listened to this advice and acted like a good economist. They would have known that there is a good chance that their future income will decrease and so they would have known that their present value of lifetime resources (their net income over their life) will decrease. This in turn would cause them to decrease consumption slightly. So now lets say at the age of 30 a person was able to earn to $400,000 for the rest of their life and they intend to only live to be 70, so they would spend $400,000/40= $10,000 per year. But if they see that over the next two years their income decreases by $10,000 in each year, that doesn’t mean they decrease consumption by $10,000 each year. Instead their new smooth consumption would be 400K-20K/40 = 9.5K, so instead of decreasing their consumption by $10,000 for two years they decrease their consumption by $500 for the rest of their life.

Consumption Smoothing

So a Good Ismaili would listen to this sound economic advice to live frugally and reduce consumption; thus acting like a good economist. (In case you were wondering, the opposite does not hold, a good economist doesn’t make a good Ismaili).

Partial Equilibrium Persuasion

In one of my classes I had the opportunity to listen to a guest lecturer from someone who heads Stanford’s recycling department. She talked to us about recycling and why its important. And she came up with ‘Top Ten List’ for reasons to recycle (hopefully in a future post I’ll discuss why I dislike such lists). But the top two reasons on her list were: 1. Its good for the economy and 2. It creates jobs (a bit redundant I might say).

But her point was that when we recycle you employ someone to collect the waste, someone to receive it, someone to filter it, someone to process it, someone to sell it, and on on… she said around 10 jobs are created for each tonne of waste we recycle. Sounds like a good idea right? We recylce, and create jobs, a win-win for sure!

I hope my sarcasm was conveyed in that last sentence. This is too simplistic and a partial equilibrium analysis. Now I’m all for green-collar jobs and such, but lets say we didn’t have any extra unemployment (nothing above the rate of natural unemployment). Would this still be a good argument? If the economy is in a state of equilibrium such partial equilibrium analysis should only be taken with a grain of salt. If there is no involuntary unemployment, everyone has a job, so her second argument is total BS since a recycling program isn’t creating jobs but rather just reallocating labor from one job to the next. There is no net change in employment.

But her first point may be true, it could be good for the economy and society as a whole. That is only if people choose to actually gain employment in recycling professions. If people already have jobs, why would they move to a recycling-related job? For the vast majority of people a big incentive would be higher wages. And general production theory dictates that we pay wages that are equivalent to the marginal productivity of labor. So people will only earn higher wages if they their labor is more valuable and by the income approach we can see this reflected in a larger GDP.

The cobb-douglas production function for an entire economy is as following:

Where Y is GDP, K is capital, N is labor and A is any total factor productivity but most commonly referred to as technology. An increase in GDP due to recycling would be included in the A component since N has not changed but is more productive (lets assume that capital stays constant too or has negligible change due to recycling jobs).

But this is all contingent upon the premise that recycling related jobs are better paying than other jobs. But since there is such a variety of jobs that are related to recycling, its hard to say whether recycling will actually be better for the economy. For example, its easy to say that creating trash collector jobs isn’t going to be a great investment for our economy. But what if a bicycle-maker can produce more bicycle thanks to higher recycling of metal scraps, what if the firm is growing so rapidly it needs another high-paid manager. Such jobs will increase productivity of labor (assuming marginal productivity of labor is equal to wage) and help the economy. But its really hard to tell whether the sum of all jobs created by recycling is really better for the economy compared to the jobs people previously held. So until then I cannot give a definite answer.

In conclusion, yes recycling is good for the economy and in the current state with so much unemployment it could possibly create jobs. But the moral of the story is when people make such claims, do take them with a grain of salt because if the unemployment rate would not have been as high, this analysis may not hold.

The Business of Sperm-Banking

I wrote a piece on the “Objectification of Sperm Banking” and the economics behind it. I thought I’d piece together a few parts of my paper in order to summarize it:

$$ SPERM DONORS WANTED $$ Earn up to $1,200/month.

Give the gift of family through the California Cryobank’s donor program

The Stanford University newspaper has been printing the above advertisement for several years. In order to make it easier for students to join the donor program, the California Cryobank has strategically positioned a deposit collection facility on the Stanford University campus. Why does the California Cryobank desperately want to recruit Stanford students? This particular sperm bank has been in the business long enough to understand that most mothers strongly prefer the sperm of a well-educated man, such as a PhD candidate at a prestigious university, to the sperm of a high-school dropout. And this is why the Cryobank recruits students almost exclusively at prestigious universities: to conform to consumer preferences and reach a wider audience. One of the Cryobank’s founders said, “if our customers wanted high-school dropouts, we would give them high-school dropouts”. The growth of the sperm marketplace has been a recent phenomenon in the history of artificial insemination, and has been made possible by our treatment of sperm as a tradable commodity.

The rise of the American sperm banking industry

In 1884, Dr. William Pancoat successfully inseminated an infertile woman using the sperm of one of his medical students. Since then and until the 1970’s, only medical research universities practiced artificial insemination by donor (AID), initially for academic research. As awareness and the success of these practices grew, infertile couples flocked to doctors for this reproductive treatment. The process of AID in its early days was very crude. A couple would consent to the doctors terms of insemination, and then the doctor would choose a medical student from his or her class that most resembled the husband. This resemblance criterion was only established so that the donor-conceived child would appear similar to the social father and preserve the secrecy of the procedure. Secrecy was in the best interest of the couple so as to avoid both the stigma surrounding the husband’s infertility and legal repercussions.

The formation of formal sperm banks would not be possible until the 1970’s, when the legal and technological structures had finally been put in place. The University of Iowa established the first sperm bank in 1953 following the discovery of cryopreservation. This technology allowed the freezing and thawing of sperm – essentially the ability to store the sperm until a later date. Also around this time, a geneticist named Sheldon Reed developed a screening test for semen . These two technological innovations allowed for the creation of banks that could store genetically superior sperm. Soon, legal restrictions would also slacken and gave way to the establishment of formal sperm banks. In 1973 the Uniform Parentage Act was instated, and this law gave the paternal rights of the donor-conceived child to their social father. Despite the fact that all legal and technological barriers had been removed, only slightly over 10 sperm banks existed in the early 1970s. In 1978 an article was published in the American Fertility Society’s Journal that described how despite having the ability to freeze donated samples, “the commercialization of sperm banking has not been developed”. The industry had yet to take off.

The Nobel Prize Sperm Bank – An Experiment in Eugenics

The number of sperm banks eventually grew to 135 by 1990, and today at least one can be found in every state. But it took twenty years for sperm banking to become a widespread service. What led to the realization of sperm’s commercial potential? The drastic transformation of the sperm banking industry began with the opening of the Repository for Germinal Choice, otherwise known as the Nobel Prize Sperm Bank.

Robert Clark Graham was the founder and visionary behind the Repository for Germinal Choice. He used the repository as a way to pursue his passion for positive eugenics, which is the practice of selective breeding with the aim of improving the human race. Graham justified the sperm bank that he found in 1971 by claiming that the Darwinian notion of natural selection had been defied by our society. Graham reasoned, “cradle-to-grave social welfare programs paid incompetents and imbeciles to reproduce”. To save the human race from a “genetic catastrophe”, Graham founded the Repository for Germinal Choice, which recruited only donors with the highest genetic potential. In Graham’s eyes these donors were mainly Nobel Prize laureates and henceforth the sperm bank had been dubbed the Nobel Prize Sperm Bank (NPSB).

Though Graham’s eugenic beliefs may have been extreme, he has had numerous benefits for the growth of this industry. Graham was obsessed with providing women with only the best of sperm in order to produce the smartest and healthiest babies. For his donors it meant that they “endured physicals and endless blood tests. They completed massive medical family histories. [And any] serious illness disqualified them”. Charles Sims, one of the founders of the California Cryobank, conceded that the repository “changed the face of sperm banking forever”. Sims described how at the time most sperm banks told the mother only the eye color, hair color and blood type of their donor. Graham, on the other hand, gave mothers full control to choose their donor. He introduced donor catalogues, which profiled not only the biological but also the social characteristics of the donor. For example, the profile page of Donor Red describes how this donor was an “Outstanding physicist at a large university,” he had a “Nice appearance, winning smile” and was “happy and radiant”. This information was provided in addition to his biological data such as height, weight and hair type. Graham might not have known it then, but he had inadvertently revolutionized the business of selling sperm.

David Plots, the only historian on the NPSB, uncovered that the majority of Graham’s customers worked in healthcare or counseling. This was no coincidence and Plotz found that “health-industry parents preferred the repository to other sperm banks because it screened candidates carefully for genetic and other illnesses”. The health benefits, coupled with the newfound agency given to women, started a consumer revolution within the sperm bank industry.

Many more for-profit sperm banks were established after the Universal Parentage Act. The California Cryobank, now the world’s largest sperm bank, was founded in 1977. The Cryobank, like many for-profit sperm banks at the time, sought to attract customers but did not know how. Sperm banking was a new industry and many of its basic market practices had yet to be established. Though the NPSB was never considered a financial success, women had begun to express a preference for this particular sperm bank and it’s popularity had grown steadily over the years. The California Cryobank, along with other sperm banks, had become sensitive to consumer preferences and anxieties, which led them to understand the appeal of the NPSB to women. As an economically strategic decision, the California Cryobank followed the NPSB’s lead and gave customers both donor catalogues and health guarantees; and soon they too saw the benefits of these practices. Eventually many more sperm banks adopted these strategies, though this process of adoption was slow and it took a few decades until they came to fruition.

Through a rigorous process of iteration, the Cryobank developed more advanced medical and advertising practices and grew to become the industry leader. Today, it’s customers extensively search for donors on their website and can order frozen sperm directly to their hospital rooms. Customers can evaluate donors by purchasing extra essays, audio interviews and even a description of their facial characteristics. The few innovations by the NPSB made sperm banking a consumer-centered practice, and this eventually sparked the consumer revolution that has changed the practice of sperm banking today. After adopting these innovations the California Cryobank has demonstrated that sperm banking can be a lucrative business; which has led to the rise of more than a hundred sperm banks open since 1975.

If you’d like to read the entire paper, shoot me an email!

Soccer Transfers and Game Theory

Soccer is a fascinating sport. Yes its fun to play, and it is definitely the most popular sport in the world, but at the professional level its a whole different game. And that’s because the manager plays a much more important role at the professional level. A good manager can compensate for a lack of talent in the team. Soccer strategy can be the reason why the underdogs come out on top (shout out to Jose Mourinho for winning the Champions League with Porto in 2004).

But the reason why I’m super fascinated with this aspect of professional soccer is that I, along with most people, don’t quite understand what good strategy looks like. How exactly do you create a synergistic formation for your team given your players? How do you render an oppositions tactics useless by planning in advance? How exactly do you know which player to play and when to play them for maximum performance in your match? If you can answer these questions on a macro-level, then you’re a legend in the making.

I have yet to write up a number of soccer theories and commentaries that I may have, but I thought I’d start with some basic game theory that I recently read about. While reading my daily dose of SkySports Soccer News, I came across this link where Man City apparently ‘bullied’ Totenham into pulling out their bid for Criag Bellamy.

Now here is a game theoretic analysis of the situation, since Man City has an unlimited supply of money (those bastards) they were able to use their financial power and control this ‘game’. They essentially played an ultimatum game with Tottenham by threatening to purchase Wilson Palacios, another target for the Spurs (for those not acquainted with soccer, Spurs is the nickname for Tottenham), unless Tottenham dropped out of the race to sign Bellamy.

Now there are a few things to note. At the time, City had bought De Jong, another midfielder and hence weren’t really looking for a midfielder so this threat may not be completely credible, but since City do have all the resources in the world I’m sure they would have welcomed a good midfielder and the opportunity to send a message to all potential competitors that they should not try and go up against City when trying to sign a player.

I’ve made a Decision Tree diagram below, though this is not completely accurate because I’ve assumed that by bidding for Bellamy, Tottenham will actually manage to sign him. To make this diagram more accurate we would need probabilities of Bellamy wanting to join Tottenham and add another decision node, but I’m not willing to speculate on these probabilities and I’m going to assume there was a very high chance of this happening which is why City had to threaten Spurs.

So according to this decision tree, what is the optimal choice for Tottenham? Lets use backward induction to deduce the subgame perfect Nash Equilibrium:

If Tottenham bid for Bellamy, Man City’s best option is  to sign Palacios (assuming that in the long run they aren’t making a loss through this transaction since Palacios isn’t too similar to De Jong and could really add to the City side). But if Spurs don’t bid, then City’s best option is to not sign Palacios since they don’t really want him. So what should Tottenham do? In both scenarios they get one player, so they should pursue the option that gives them the player they want the most. By the result, we can assume that player was Palacios (though in reality I think we should have added another decision node to consider the possibility of alternative players that would have come to Spurs had they not signed Bellamy, and in reality we know Defoe was one of these alternatives).

So the sub-game Nash Equlibrium was for Spurs to not bid for Bellamy, and for City to sign Palacios if they Spurs did bid, and to not sign Palacios if Spurs did not bid. The expected outcome is for Spurs to not bid and for City to not sign.

By this logic the threat “You know, if you don’t drop out of Bellamy, we’ll sign Palacios too and you won’t get either of them” is not credible. But that is under the assumption that Bellamy was more likely to sign for Spurs (if he wasn’t then why would Man City threaten Spurs?).

We also should evaluate the assumption that City would benefit from signing Palacios. He would have probably cost them around £ 14,000,000 which is what Spurs paid for him. Would that amount be worth how much Palacios would add to the team, and the message for other teams to not mess with City? That depends on the City management team, if yes, then the sub-game Nash Equilibrium we found was valid. If this assumption is not true, then Spurs should have just gone ahead and bid for Bellamy and Palacios and were likely to sign both.

Another assumption I made is that Palacios would definitely be signed by City if they wanted. I’m not going to question this one since I don’t know too much about the actual situation.

Anyways, given how complicated this apparently simple situation was, I can only imagine how hard it must be for coaches to design the perfect formation to compete in the Champions League Final.

And as an afterthought I’d like to apologize to all who I may have offended by referring to football as soccer in this post.