An ARBITRARY post: Library reminder

So I got this in my inbox - and I am posting this up as an arbitrary post so that I am updating my blog!

REQUEST NOW AVAILABLE.
The material you requested
is now available for collection
from the listed location. It will
be kept for you for 7 days
from the date on this notice.

AUTHOR: Osborne, Martin J.
TITLE: An introduction to game theory
CALL NO: QA269 .O78 2004
BARCODE: xxxxxxxxxxxxxxxxx
LOCATION: xxxxxxxxxxxxxxxxx
PICKUP AT: xxxxxxxxxxxxxxxxxxxx

Martin Osborne baby!!! Yeah baby yeah! A famous game theorist.

Why I am Single: An Economic Explanation

The theory and empirical work around human behaviour is generally in the realm of microeconomics (macroeconomics is the aggregation of microeconomics). And so this is the post on microeconomics which I said I would post in the previous post I posted.

Currently, I am in my final year of my undergraduate economics degree, and it is getting increasingly stressful. If I were to be asked why I am not in a relationship, if I want to be in a relationship, or when I want to be in a relationship, I would reply: (i) no time (ii) not at the moment (iii) not anytime soon. These more or less revolve around the concept of the limitations on my time, because of the workload I have to do at uni.

In economics, apart from thinking of time constraints, we can think of utility and cost (or disutility). Utility is sort of analogous to the 'happiness' I get from being in a relationship (utility covers more than happiness). Cost is the cost of being in a relationship.

Now, given my current situation, my cost function is a quadratic function, perhaps an arbitrary
C = 50t - 2.5t^2 where t = the time period, starting from zero. Let us assume that each unit of t represents a semester at university. Hence, t = 1 is the first semester of the first year; t = 2 is the second semester of the first year, and so on.

If I differentiate this equation with respect to t, I derive my marginal cost function, which is:

MC = 50 - 5t

Now, given my current situation, my utility function is also a quadratic function, perhaps an arbitrary

U = 1.5t^2

If I differentiate this equation with respect to t, I derive my marginal utility function, which is:

MU = 3t

Now, to maximise the utility I get from being in a relationship, I need to set MC = MU (this is an economics condition that is used for profit maximisation in firms).

Hence,
MC = MU
50 - 5t = 3t
8t = 50
t = 6.125

Hence, I would maximise my utility from being in a relationship after I graduate! Remember that each t represents a semester. There are 6 semesters in an undergraduate degree, and so a t of 6.125 implies that it would be most profitable for me to enter into a relationship after I graduate, perhaps a month or 2 after I graduate. Prior to t = 6.125, the marginal cost (disutility) of being in a relationship exceeds the marginal utility, or phrased differently, the cost of being in a relationship exceeds the benefit.

And this explains why I am still single!

Failed Experiment!

Okay, so like none of the other people with the same name as me responded... but nevertheless, that's okay!

My next post will be an interesting topic... with microeconomic foundations!

How many of you are there out there, and how similar are they to you?

Yes a rather odd question for a title. Basically, one night (tonight, in fact), I decided to Google my name to see what turns up. I'm doing this not for pride's sake, but rather that there is an increasing trend for employers to want to Google potential employees to see what they're like - this involves visiting their MySpaces (I have none), blogs (only this one), Facebook (which I have, but hardly use because I spend most of my time with either uni work or research work), Friendster (which I had a looong time ago but which I will delete... soon... if I remember!). Of course, any pictures or comments or videos that you post is visible to the public (depending on your settings), not that I post anything offensive, but just be aware that employers might have a look around.

To those I have written to on their blogs: Hello! I wrote hello note(s) on your pages just to say hello and am wondering if we share anything in common. I initiated contact for the sole purpose of getting to know other people who have the same name as me, nothing else, but pure friendship. To those who got the mail, feel free to leave a comment to this post if you wish :-)

Game Theory: WHY!?

How ironic that since last semester, I thought, oooh yes I would LOVE to do game theory. I understood that it involved quite a fair bit of mathematics, but I thought that I could possibly manage. The first week of class was easy - just a revision of some common games, including the infamous Prisoner's Dilemma. But then the second week came, and that was a killer because I realized one important thing... math is INsufficient (what a shock, I know!) for game theory; one also needs to have strong skills in figuring diagrams out when the explanations somehow don't do the work... and I have read the prescribed chapter of the book, and I think if I were to read it twice, it wouldn't help get me from understanding nothing to understanding something! What a shock this class has turned out to be, but I, determined to be some sort of a future microeconomist, have to hold on I suppose. If this is only week 2, I am dreading week 3!

This brings me to a question I really should ask myself: Do I REALLY want to become a game theorist, or a microeconomist for that matter?!

Politics: Whitman's lecture on political economy

The pdf is from his website, here.

Of interest: Glen Whitman's post on incentives

I think this post is highly interesting. Reason: a basic assumption of microeconomics is that people (economists call them 'economic agents') are motivated by incentives. Common sense, no? Whitman was outlining the point that incentives might not work in the way in which we might predict, because economic agents aren't robots basically - they are tempted to cheat, to evade the law, etc, so these need to be accounted for when introducing incentives.

Have a read here.

Notice: On Hiatus!

Hi to all who read this blog... as you have noticed, I have been updating my blog less often than normal. I have a very good reason for this - the upcoming exams! But I might do some random posting when I get bored studying.

In any case, for those having assignments, exams, all the best!

Schumpeterian Economics: Introducing, Information Economics

The economics of information is a relatively new thing I am currently studying. One interesting quote is from Boyle (1996, p.38 as cited in Dempsey, 1999, p.33):

[Incentive] analysis largely ignores the opposite perspective, that of the free flow of information. If we switch the perspective, we can see that one important purpose of [intellectual property] law is to make sure that future creators have available to them an adequate supply of raw materials. From this perspective, too many ‘incentives’ could convert the public domain into a fallow landscape of private plots.

Basically, we are pretty used to thinking that information is a public good, and hence to protect the profit incentives of firms investing to create information, governments put intellectual property laws in place. I will update this more later on.

Of Interest: The importance of preparing for your tax return early!

This is understandably quite a random post. The reason for this is that I was assisting my research doctor with compiling receipts to prepare for his tax return. Since he has been busy with other stuff, he's been unable to complete it for the year, which means that my job was to compile receipts together and then match them to the relevant banking statement. Wow. Imagine, if once I start working, I have to do something like that. So, here is a gentle encouragement/threat to myself and to readers, please, please, please, PREPARE FOR YOUR TAX RETURN EARLY! I hereby salute all the office, personal, etc assistants who do those jobs.

Experimental Economics: Double auction vs Posted offer

As a short intro, both double auction and posted offer are market institutions (which is basically a specification of the rules of trade in a market). Let us assume that buyers want to buy and sellers want to sell a specific good, for instance, shoes.

In a double auction institution, buyers bid upward for the shoes and sellers bid downward to sell their shoes, and then a trade happens when these meet. For example, I want to buy the shoes for $5, and then a seller wants to sell it for $7. So then I say '$5.50!' The seller might find it too low and go 'Ok, ok, $6.50'. It goes on and on until we agree on a price. The double auction institution is in fact highly efficient, as it yields the maximum efficiency in trade (this is measured as the economic surplus from the trade divided by the total potential surplus. Economic surplus is calculated like this: for buyers, this is the price you pay minus the price you would be willing to pay for it; say I wanted to pay $6.50 for the shoes but I got it for $6.00, then my surplus is $0.50. Similarly, for sellers, this is the price you receive minus the price you were willing to sell it for; say you were willing to sell the shoes for $5.80 but got $6.00 for it, so your surplus is $0.20).

The posted offer institution is as follows: sellers post a price, and then buyers see the price and decide if they want to buy or not. No bargaining, just a posted price. This tends to be less efficient than the double auction, as maybe some sellers would have been willing to sell for $0.50 less (and possibly make a trade), but cannot bid down due to the price being fixed.
A class experiment would confirm this result. It is actually a rather fun* experiment. In fact, if you're planning on having a birthday party, I would recommend this as an icebreaker or a game in the party. Perhaps I really am too much of a scholar.

*according to my individual preferences

Of Interest: Have you ever noticed that many of the world's smartest are Jews?

In fact, I was actually wondering about this. I remember, prior to commencing my Economics degree and preparing for a scholarship interview, the results of the winners for the most recent Nobel prize (at the time) was released. Of interest to me were the winners for their game theory, Aumann and Schelling. Ariel Rubinstein, a famous microeconomist, is a Jew (haha, the last name gives it away). And I thought, wow, why is that the case? I found an article from Commentary Magazine here, which I found a good read. It really makes you think. The article made me go wow.

Game Theory: Beauty Contest (Ooh!)

A quote from Keynes, 1936, p.156 regarding the levels of thinking regarding beauty contests:

"It is not a case of choosing those [faces] which, to the best of one's judgment, are really the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees."

Have a wiki about the beauty contest here.

History: Israel and Palestine

I found this link while browsing through Harry Clarke's blog, and had a read at it. It is highly interesting - seeing the differences between what is reported in the media, and what the real story is behind the scenes. Have a read here, posted on the online commentary magazine.

Music: Darin Zanyar

It is rather evident, after this posting, that I am in fact, a female! This is the runner up of the 2004 (if I remember correctly) Swedish Idol, Darin Zanyar.

His lyrics are rather well... as one would expect from European artists (no offense to them, I enjoy European music)... but the beat and arrangements are good, in my opinion.

Visit Darin's official homepage here (in Swedish and English)

Experimental economics: Price Matching Guarantees (2)

Hi again everybody (so far it seems no one has left any comments... but let's move on)
This is the update regarding Price Matching Guarantees (PMGs), where one seller promises to match (note: match, not beat) its rivals prices, as seen in supermarkets or bookstores. I will recap the theory again. When a seller says that he/she will match its rivals prices on a product, it seems like such cut-throat competition, doesn't it? The truth is that it is anti-competitive. Think about it this way. If I sell my product for $70 (assume a price range of 1 to 100), then if you sell yours for $65, you will service the entire market demand for that good. However, if I promise to match your price of $65, then we both split the market. Since that's the case, we might as well tacitly collude (in layman's terms, cooperate non-formally) and set our price at $100 and get even more profits. There's no point in you lowering your price to $60 if you know I'm going to match it - and hey, that means lower profits for the both of us! (Assume that the number of buyers and products on the market remain constant). So, we might as well keep a high price. And that is the anticompetitive nature of PMGs.

There are many assumptions that come along with the theory of course (which was first noted by Salop, 1986). I will skip them, but the main point to note is that we are assuming that it doesn't cost buyers anything to invoke the guarantee. BUT, other authors have noted that if buyers have to incur some sort of 'hassle cost' - i.e. such as fill in forms, go back to the shop and ask for the guarantee slip, etc, which cost money - then buyers would rather just buy from the seller that immediately offers the lowest price on the market, regardless of if its competitor chooses to match its price. In such a case, the game unravels and the predicted competitive equilibrium is equal to marginal cost (in this case, the lowest price of $1). True enough, the experimental data confirms this convergence towards the equilibrium price, although full convergence does not necessarily happen.

See: Dugar and Sorensen (2006) for example (sorry I can't link the article here due to copyright)

Statistics: Maximum Likelihood

Ah, the infamous maximum likelihood - what I've been waiting to study all semester for a stats subject I am currently taking. I normally don't use Wikipedia and read journal articles instead, but I love the simplicity of everything in Wikipedia. I tend to think that Wikipedia is fine for basics. So, read about maximum likelihood here.

Microeconomics: Bounded Rationality

I've read a few journal articles that keep mentioning the term 'bounded rationality' somewhere, and I have wondered for the longest time what that actually is! If I read correctly, it's basically that in classical economics, we have assumed economic agents as having perfect rationality - they will not do anything that would violate their preference ordering, etc, basically being perfect, non-contradictory, always utility maximising in their choices. Of course, such a perfect agent does not exist in reality. Consequently, there have been people (whose names have slipped my mind for the moment, sorry!) who pointed this out and then developed models for bounded rationality - accounting for the fact that economic agents are not perfectly rational. Have a wiki at 'bounded rationality' here or check out this reading about modeling bounded rationality by Ariel Rubinstein here.

Statistics: Multivariate = Bivariate normal distribution?

True, only if n = 2.

Formula for the multivariate normal distribution:

If is non-singular, then the distribution may be described by the following PDF:

where represents the variance-covariance matrix.


Formula for the bivariate normal distribution:

In the 2-dimensional nonsingular case, the probability density function (with mean (0,0)) is

where ρ is the correlation between X and Y. In this case,

.

The above matrix gives a hint of how to solve the problem. In fact, I had to do this exercise for a class assignment. The proof took 3 pages long, using various statistical definitions and theorems! My proof was just meticulous and long, and I am sure that 1.5 to 2 pages should suffice. It is an amazing feeling to solve such a problem as that.

Have a look at the multivariate normal distribution page on Wikipedia, from which I copied and pasted the above formulae.

Behavioural Economics: A good link!

http://harvardmagazine.com/2006/03/the-marketplace-of-perce.html

A fabulous read!

Microeconomics: Modelling Procrastination (2)

Hi all, pardon my brief departure. I have been working on an essay assignment about procrastination which is due in 3 days, and so have been slaving over that. This entry is about the main points of 2 articles I have read regarding procrastination. They are by O'Donoghue and Rabin (1999) and Fischer (1999) (I cannot link the articles here as they are in subscribed journals).

O'Donoghue and Rabin basically aim to model procrastination by showing present-biased preferences, where individuals are impatient and favour now over later. They use a mathematical formula and calculations to derive their results. Fischer also uses mathematical models to construct her ideas, but hers come with diagrams of marginal utility and what happens when the discount rate changes (and hence when the rate of time preference changes), and we can see procrastination visually. Both are technical papers, but the intuitive result is this: it is the individual's perception of their own impatience or their own subjective valuation of their discount rates that makes them procrastinate.

How interesting! The question that remains is, what exactly is our individual discount rates?!

Microeconomics: Bernoulli and von Neumann-Morgenstern

These people did paramount work on utility functions and expected utility theory.

Rather than give their backgrounds, I thought that I would write their contribution instead.

First was Bernoulli, who formulated a utility function over an individual's wealth. Utility over wealth changes as the wealth level changes. Have a think at this: if you are broke, $100 is worth much more to you than if you were $1,000,000 rich, and were offered the same $100.
Bernoulli therefore put forth the notion that an individual's subjective valuation for a certain sum of money was not necessarily the same as the objective valuation.

What von Neumann and Morgenstern did was to extend Bernoulli's utility function to define expected utility over lotteries, but with several premises (see the previous post on the preference axioms). Their utility function is called the von Neumann - Morgenstern utility function, or more commonly, expected utility function.

In the first stages, one can only think of utility as being ordered (i.e. ordinal utility). For instance, if the utility of a certain commodity bundle, x (I shall use commodity bundles for the moment, as wealth must generally be mapped as a density function because of its continuous nature) is subjectively higher than the utility of another commodity bundle y, intuitively,

U(x) > U(y)

Fortunately, once we have the expected utility form (which satisfies the independence axiom, a.k.a. independence of irrelevant alternatives), we can then start to think of the notion of utility as being a cardinal form (i.e. one with real values). I will not go through the proofs here, but it is pretty easy to check them out on the web.

Hooray for the expected utility form!

Microeconomics: Preference Axioms

My goodness, I am so pleased! While surfing the net for some information on the Bernoulli utility function (used in statistics and microeconomics), I stumbled upon a fabulous website that listed the preference axioms of expected utility theory perfectly. I have cut out and pasted a section here, and the entire page (with lots of really amazing stuff!) is from econport, at http://www.econport.org/econport/request?page=man_ru_basics3. It is just amazing how simple they have made the axioms!
-----------------------------------------------------------------------------------------------------------------
The Preference Axioms

In order to construct a utility function over lotteries, or gambles, we will make the following assumptions on people's preferences. We denote the binary preference relation "is weakly preferred to" by , which includes both "strictly preferred to", and "indifferent to".

Completeness: For any 2 gambles g and g' in G, either g g' or g' g. In English, this means that people have preferences over all lotteries, and can rank them all.

Transitivity: For any 3 gambles g, g', and g" in G, if g g' and g' g", then g g". In English, if g is preferred (or indifferent) to g', and g' is preferred (or indifferent) to g", then g is preferred (or indifferent) to g".

Continuity: Mathematically, this assumption states that the upper and lower countour sets of a preference relation over lotteries are closed. Along with the other axioms, continuity is needed to ensure that for any gamble in G, there exists some probability such that the decision-maker is indifferent between the "best" and the "worst" outcome. This may seem irrational if the best outcome were, say, $1,000, and the worst outcome was being run over by a car. However, think of it this way - most rational people might be willing to travel across town to collect a $1,000 prize, and this might involve some probability, however tiny, of being run over by a car.

Monotonicity: This big ugly word simply means that a gamble which assigns a higher probabilty to a preferred outcome will be preferred to one which assigns a lower probability to a preferred outcome, as long as the other outcomes in the gambles remain unchanged. In this case, we're referring to a strict preference over outcomes, and don't consider the case where the decision-maker is indifferent between possible outcomes.

Substitution: If a decision-maker is indifferent between two possible outcomes, then they will be indifferent between two lotteries which offer them with equal probabilities, if the lotteries are identical in every other way, i.e., the outcomes can be substituted. So if outcomes x and y are indifferent, then one is indifferent between a lottery giving x with probability p, and z with probability (1-p), and a lottery giving y with probability p, and z with probability (1-p). Similarly, if x is preferred to y, then a lottery giving x with probability p, and z with probability (1-p), is preferred to a lottery giving y with probability p, and z with probability (1-p). Note: This last axiom is frequently referred to as the Independence axiom, since it refers to the Independence of Irrelevant Alternatives (IIA).

The last axiom allows us to reduce compound lotteries to simple lotteries, since one can also be similarly indifferent between a a simple lottery giving an outcome x with a probability p, and compound lottery where the prize might be yet another lottery ticket, allowing one to participate in a lottery with x as a possible outcome, such that the effective probability of getting x was p.

Statistics: Poker Probability

Have you played a game of poker and think, hmm... what are my chances of winning? Well, a friend of mine brought me to a page in Wikipedia that had a fabulous listing of poker probabilities. I copied the following picture from this link: http://en.wikipedia.org/wiki/Poker_probability. Have a look and a marvel here, or go directly to Wikipedia.

Visual help	Hand	Frequency	Probability	Cumulative	Odds	Mathematical expression of frequency
	Royal flush	4	0.000154%	0.000154%	649,739 : 1
	Straight flush (excluding royal flush)	36	0.00139%	0.00154%	72,192.33 : 1
	Four of a kind	624	0.0240%	0.0256%	4,164 : 1
	Full house	3,744	0.144%	0.170%	693.2 : 1
	Flush	5,108	0.197%	0.367%	507.8 : 1
	Straight	10,200	0.392%	0.76%	253.8 : 1
	Three of a kind	54,912	2.11%	2.87%	46.3 : 1
	Two pair	123,552	4.75%	7.62%	20.03 : 1
	One pair	1,098,240	42.3%	49.9%	1.37 : 1
	No pair / High card	1,302,540	50.1%	100%	0.995 : 1
	Total	2,598,960	100%	100%	0 : 1