$1138.25/$1350 after Stoke drew Hull yesterday - the EPL is certainly getting more "artistic" as a rule. Why spoil a good thing?
$25 on Chelsea to draw Arsenal (at 3.30)
$25 on zero goals in Chelsea vs Arsenal (8.00)
Saturday, Nov 29, 2008 - 19:45 SGT Posted By: Gilbert
Three Fifths Through
Well, now I know what the paper recycling bins outside the multipurpose (i.e. examination venue) sports halls are for - for students to conveniently dispose of unneeded notes the moment they step out. Or were they plain rubbish bins?
General Biology wasn't too bad I suppose, but with a good portion of the questions being simply statements of facts (i.e. what family does this organism belong to, and the like), and being an open-book examination on top of that, I suspect that the difference between grades is going to be minute. Oh, my textbook and notes knew how to do about half the paper too; no scholarship for them either, regrettably.
A few tricky questions, and more than a bit of referencing assignments (Hint to future batches - bring those! One question probably couldn't be answered from the textbooks and notes, and would essentially be a toss-up unless you're a complete Biology geek to start with, but then you wouldn't be needing cheap hints)
Rewarded myself with $1 ice-cream-on-a-slice-of-bread on the way home. The icy chocolate milk will come later. Life' little comforts are certainly agreeable.
No luck at all with pretend football betting, now at $980.75/$1300. Then again, I figure nobody much got anything out of last week either. Manchester derby's tomorrow, and for today:
$50 on Stoke City to draw Hull City (at 3.15)
And out of nowhere, here's Bruce Lee playing ping pong with nunchucks. Got to try that one day.
Friday, Nov 28, 2008 - 00:43 SGT Posted By: Gilbert
Xams
Health Economics and Game Theory are done and dusted (what's with holding them all the way at Sheares and Kent Ridge Hall respectively, anyway?), and I guess I'm probably okay for both (N.B. I'm usually slightly optimistic towards examinations, unlike some who appear damn sad after omitting a full stop, but that's another story).
Probably could have done a bit better for Health Economics had I spent more time on the final (short essay) question instead of spending time to confirm MCQ answers for options that were virtually eliminated, but that's hindsight. For Game Theory, indeed no proofs appeared, with the main focus being on finding perfect Bayesian equilibria (including one on Nim); I think I got most of the stuff correct, but didn't manage to finish writing the answer for the last question (after showing most of the working). Sigh, for just a minute more - now I don't know whether this is worse than realising the answer only after the examination ends.
I suppose I'm pretty lucky to be mostly "fast enough" for examination purposes, as there probably are people out there who are quite brilliant but just cannot or will not calculate quickly (as a former teacher of Grigory Perelman [of Poincaré conjecture fame] said, "...he was not fast. Speed means nothing. Math doesn't depend on speed. It is about deep.") And indeed in the real world, "all the exams are open-book, and they don't have time limits".
Well, just for interest, here's the last question (heavily modified since I don't know if direct reproduction is acceptable, but the spirit is there):
Two players, A and B, are playing a promotional card game with a dealer at the Marina Bay Sands. The game is as follows:
The dealer puts two cards in front of each player (four cards in total for both players). One of these cards is an Ace, and the other is a Joker.
Each player picks one of the two cards (thus both may have Aces, both may have Jokers, or one may have an Ace and the other a Joker), and looks at it privately.
Then, each player may choose to continue the game or fold (they make this decision simultaneously and do not know whether the other player continues or folds. You can think of them submitting an envelope to the dealer with their card if they want to continue, and an empty envelope if they want to fold).
If the player folds, he does not have to pay anything, but also cannot win anything.
If a player continues, and the other player does not, the player that continues wins $10 from the dealer.
If both players continue, their cards are revealed, and the outcome is as follows:
If both players have an Ace, they both pay the dealer $2.
If both players have a Joker, they both pay the dealer $5.
If one player has an Ace and the other has a Joker, the one with a Joker pays the one with an Ace $5.
What is the optimal strategy that player A should pursue? (Possible AAAAA for good enough answers up for grabs!)
Skipping a 3:30 a.m. Champions League game due to the game theory paper at 9 a.m. would have been a big sacrifice on my part, had it not been yet another nil-all draw (which sent both United and Villareal into the knockout phase, though).
After the amusing incident involving a certain Gerrard some weeks back, Wayne Rooney has seen fit to emulate his Scouse pal with a rather lame effort (see 5:40 in the video above) despite starting that move brightly with a clever backheel. I don't know how honest Rooney really is (at least he promptly apologized for the incident), but he certainly sucks at diving - if you want to cheat, you may as well learn from the masters. His frustratingly long layoff from scoring (which began right after I ate my words about him) probably contributed.
Well, on to the open-book General Biology. Hope I do well here.
Tuesday, Nov 25, 2008 - 00:17 SGT Posted By: Gilbert
It continues to lie motionless on its side, with a "feed me" look
Examination Number Two is EC3312 Game Theory And Applications To Economics, a module aptly named as game theory is useful in other fields as well (though with all this cross-fertilization going on, watch out for EV1101 Everything You Need In Life). I have ventured an introduction to the subject over a year ago, with some schooling from the second half of Microeconomics II, and a bit of self-study, and while there is some overlap with that and a few other modules, EC3312 must be said to be more rigorous, systematic and extensive (as it should well be) in approaching game theory.
As already discussed in that year-old blog post linked above, game theory is the mathematical (rational) solution of well-defined situations ("games") under certain assumptions (yes, again). The textbook used is A Primer in Game Theory by Gibbons, with the professor following the incremental approach of the book, beginning from the simplest class of Static Games of Complete Information, then Dynamic Games of Complete Information, then Static Games of Incomplete Information, and finally Dynamic Games of Incomplete Information. To summarize (again, click to display):
Complete Info
Incomplete Info
Static
Simultaneous-move
All players' payoffs known
Simultaneous-move
Some payoffs unknown
Dynamic
Sequential-move
All players' payoffs known
Sequential-move
Some payoffs unknown
N.B. There also exists the concept of imperfect information, where one does not know about the actions of other players (at least in time for this information to be incorporated into making one's next decision). All combinations (i.e. complete/perfect, complete/perfect, incomplete/perfect, incomplete/imperfect) are possible (see Wikipedia example).
As an equilibrium concept in a stronger class of games must be true when applied to a weaker class (but not the other way around), one might conceivably just learn the procedures behind Dynamic Games of Incomplete Information and use them to solve all the given classes of problems; However, as might be imagined such procedures can be unwieldy, and quite unnecessary if a problem is known to be of a simpler class, and moreover the intuition behind game theory is probably best built from the ground up. Thus, the progressive approach.
First off, game theory is not simply some namby-pamby academic theory, as likely everyone has used it (with most probably without realising that) in daily life, whenever actions and advantages are in play. A child applies it when he tries to decide whether to lie or not to lie about snarfing the last cookie. A housewife applies it when she tries to decide how hard a bargain to drive when haggling. True, they probably don't think of numerical utilities and draw matrices in their minds, but use it they do.
Now, if only one person is involved in some situation with known payoffs, there is not much to analyse - take a guy who spots a $1 bill, a $10 bill and a $100 bill fluttering in the street. Obviously, he picks up all $111. More generally, he will just do what is best for himself (which it has to be noted implies no moralistic values on what is "best", though in economics pure monetary profit is generally assumed for simplicity).
1. Static + Complete
The simplest form introduced. Given that players each have access to a certain number of strategies, and the payoffs for each player for each given combination of strategies are fully known by all players ("common knowledge"), what should each player do? Interestingly, game theory may not always be able to resolve this issue. What game theory tries to do is to discover the Nash equilibrium, which is a situation where for all players, given the strategies adopted by all other players, they cannot do better than their own strategy.
Nash (1951) proved that at least one such equilibrium (perhaps in mixed strategies, which involves probabilistic selection of strategies) must exist (though this famous observation was dismissed offhandedly as trivial by von Neumann), for any game with a finite number of strategies and participants. If that is a unique equilibrium, then rational participants should (but often don't in reality) automatically gravitate towards it (and the "what should I do" question is answered). There sometimes exist multiple Nash equilibria, though, and in these cases game theory may not be able to serve as a rational guide for what strategy to adopt. (Personal note: Is it rational to presuppose that players with no foreknowledge of each other would then take the guaranteed mixed equilibrium strategy solution as their strategy? - for an example see the "battle of the sexes" game)
A rather elementary first step for a player would then be not to consider any strategy which in every case offers lower payoffs ("strictly dominated") than another of his possible strategies, and happily know his next step if only one strategy remains after iterating this process. This may not happen, in which case he can use a more sophisticated method of determining the (possibly multiple) best strategy reponses, for each combination of strategies, for all players. Then, if some combinations exist that are the best response for all players, they are Nash equilibria. In practice, this is often a matter of constructing a (possibly huge) matrix, and underlining the qualifying payoffs to my little Economic undergraduate's heart's content.
An infinite number of strategies is of course possible - take for example the Cournot duopoly game, where two firms simultaneously decide on the quantity to produce (even if the maximum quantity is effectively capped by market demand, any fractional number of quantity may be chosen, and as we know the number of real numbers between two distinct real numbers is infinite). In this case we reason by constructing a best response function for each firm (knowing the market demand and cost functions), equating them, and solving them simultaneously. This method can be generalized to any number of firms (as in a tutorial). Of course, writing about the procedure, actually doing the math, and doing the math under examination time constraints, are different things altogether.
Another application is the Bertrand game, where firms simultaneously decide on price (as opposed to quantity in Cournot), being able to supply any required quantity. Now if the products are identical, clearly all consumers will flock to the firm with the lower price, resulting in price = marginal cost if the competing firms share the same cost function at equilibrium (and a price just lower than the marginal cost of the higher-costed firm otherwise). Still, what was an obvious conclusion dismissed by a line or two at lower levels comes to two pages of detail in strict game theory. For differentiated products, Bertrand firms will not lose all their business if their price is higher, and in this case the treatment (and math) is much the same as for Cournot.
N.B. The graphical representation of a mixed strategy solution is only easily presented for two players with two strategies (such that two variables can be used to specify fully the best responses). For the scope of examinations iterated elimination of strictly dominated strategies thus may come into play if only to strip a scary-looking multi-strategy matrix down to a more manageable 2x2 one.
2. Dynamic + Complete
Dynamic essentially means that the players now have sequential moves, i.e. some player(s) decide on their strategies after others (and possibly observe the strategies already taken). This is the case in chess and other board games, and indeed some chess endgames would translate into a neat game tree for demonstration purposes. A general idea in solving these sort of games is through backwards induction, or beginning at the end and determining at each stage what a player would rationally do. N.B. There is theoretically nothing to stop us from solving most chess-like games through this method alone, other than the sheer scale of the required computations.
The Stackelberg model considers a dominant firm choosing a quantity to produce first, before a following firm observing that quantity and choosing its own quantity (in contrast to Cournot, where quantity is also chosen, but simultaneously). The outcome, perhaps non-intuitively, is that the following firm (now with more information) is actually better off in the Cournot game! The reason is that the dominant firm can use the following firm's rationality and knowledge against it, but producing more to begin with. The following firm is then left with the scraps at best. A little knowledge can be a dangerous thing in multiplayer games.
N.B. Moving second is not always worse. When competing on price, being second allows one to marginally undercut the price-setter, for instance.
Sequential games are more naturally presented in tree form (i.e. extensive form) as compared to matrix form (i.e. normal form), though initial equilibrium elimination is often more easily done in normal form, before the few remaining equilibria are checked for subgame perfection (as subgame-perfect equilibria must be Nash equilibria). Note that an equilibrium consists of a complete strategy even for prior strategies not leading to the player's decision node, while an outcome is just the single strategy (action) taken by each player.
With imperfect information, some players may not know when their turn comes some prior strategy taken - this might be the case with simultaneous games within sequential ones, or due to the existence of an information set with multiple decision nodes (implying that the strategies available at all nodes within the information set are identical). Note that static games of complete information are trivially transformable into dynamic games with maximal information sets for each player.
Sequential games are possibly infinitely long - the solution for an infinite bargaining game where two players take turns to offer a division of some payout (diminishing over time) is derived from the three-period game under backwards induction, under the common-sense stipulation that a player will accept a certain share only if he cannot get any better. The (finite) three period game is simple to analyse this way as the payout at the end of the third period is known.
Then, for the infinite game, the proof involves observing that the game beginning at the third period is essentially the same as that at the first (though if it actually reaches the third period, the total payout available is lower), and equating the payout for the first player with some arbitrary payoff variable; This variable may then be expressed in terms of just the discount per period (which may be different for each player). Unsurprisingly players who value later payoffs less will end up with a smaller distribution.
Note that for a finitely repeated game, the strategy taken in each stage is the same as that in a one-off game if there is a unique Nash equilibrium, and not cooperate for communal gain as some might think possible - the logic being that at the last stage, both players will surely play a selfish strategy to maximize their personal gains. But since both know that, there is no incentive to cooperate at the second to last stage, and so on to the first stage. Note however that if multiple Nash equilibriums exist, a cooperating subgame perfect equilibrium possibly involving non one-off game Nash equilibriums is possible! An intriguing variation might be when the number of stages is not fixed, but the game ends randomly.
If the game is infinitely repeated, cooperation is possible if the one-time benefit of being selfish (and triggering a similar response from the other player for the rest of eternity) outweighs the discounted infinite value stream (which has a finite value due to limits, and of course if no discounting takes place it is never worthwhile to do so). May be applied to collusion between duo/oligopolists in reality. Personal note: A slightly modified version, i.e. Tit for Tat mirrors the opponent's last move, so the punishment does not last forever but cooperation may resume if the opponent shows contrition (and some recompense) by playing the cooperative strategy again after the initial "betrayal". If there are possibly errors in playing the strategy, a version of Tit for Tat with some small chance of forgiveness is likely worthwhile. Important: Remember x + x2 + x3 + ... = 1/(1-x) for x < 1
3. Static + Incomplete
Incomplete information implies at least one player is uncertain about another player's payoff (directly cribbed from the lecture notes). While conceptually not hard to get around, the introduction of multiple possibilities (and probabilities) further lengthens the necessary calculations. For instance, for the Cournot model with one firm having private information on its own type characteristics (e.g. whether it has a high or low cost production structure), that firm now has multiple optimal strategies depending on its own knowledge, while the other firm has to hedge its strategy knowing only the probability of the first firm's type.
Note that as the probabilities are known, the obvious logical approach would be to weigh each outcome by the probability of it happening, and go for the one with the highest expected payoff (agents are assumed to be risk-neutral here); That, indeed, is the Bayesian Nash Equilibrium (the text seems to have additional examples based on normal distributions and which require more involved statistics, but this wasn't covered in the lectures). Note that mixed strategy equilibrium of a static game of complete information can be approximated by pure strategies in a properly designed game of incomplete information (by reasoning over uncertainty in the payoffs, as that uncertainty approaches zero), but I seriously doubt the examination will require a proof from scratch of this.
A second-price sealed bid auction (where the winning bidder[s] only pay the highest value bid by losing bidder[s], such as the COE) has the convenient property of allowing all bidders to simply bid their own valuation as their best strategy, without resorting to second-guessing as with the older first-price auction (where winning bidder[s] pay their own bid, and thus have the incentive to save money by underbidding if they think others have valuations quite a bit lower). N.B. The result for two bidders with valuations each randomly and uniformly distributed on [0,1] after normalization is known to be half of their own valuation. Same (relatively) complex analysis goes for double auctions where a buyer and a seller name their bid and reserve price simultaneously and have the transaction go through at the average of the two if the bid is higher than the price, since they have an incentive to second-guess each other.
4. Dynamic + Incomplete
The most comprehensive class, and one which can encompass all prior classes. Here, the Perfect Bayesian Equilibrium is defined, which requires beliefs of players within information sets containing more than one possible decision node to be specified and consistent with the equilibrium strategy whenever on the equilibrium path.
As in complete information, for pure strategies usage of the normal form game is useful to quickly eliminate impossible strategy profiles. The surviving ones can then be individually examined to see if they may satisfy perfect Bayesian equilibrium.
A common example is signalling games and pooling/separating equilibriums, coincidentally also covered in both my other economics modules this semester (Health and Labour), and also in passing here. For such questions, it is useful to think in terms of the various equilibrium combinations (often just four, for the standard Sender/Receiver roles, and two types for each of them) and see if some of them are strictly dominated or have better expectations for the given beliefs.
Went through the 04/05 and 06/07 papers, managing to do all the questions (I think). They (and the midterm) have so far been capped at a maximum difficulty level quite a bit lower than the hardest questions appearing in tutorials (free-form derivations weren't seen in the examinations, which I suppose is fairer as one can't expect to be judged overly on [lucky] creativity); I hope that continues, since some tutorial questions certainly took me more than a couple of hours to complete.
Back to Health Economics for tomorrow (today)...
Saturday, Nov 22, 2008 - 19:17 SGT Posted By: Gilbert
Practise Safety
"...require large employees to offer health insurance to their workers..."
- typo, or tax on obesity?
Will close the book on Health Economics for now, and proceed on to Game Theory (in particular the final lecture or two, for which I skipped the tutorials). Two past year exams to try out.
More security hamgineering by my uncle for the Federal Hamster Prison...
Advanced Reinforced Rubber-Band Front Gate
Gravity-Assisted Ceiling Screw Stopper
Links of the week:
generatus - a little tool for those blank Facebook status moments
God Trumps - when is this card game hitting the market? (credit: wenhoo)
Broke exactly even on last week's pretend bets, for $980.75/$1200. Thanks, United. They travel to Villa Park this week, though, and are at just 1.65 for the win (Villa at 4.45!) despite being just two places (and one point) ahead. Bad wager for me, taken either way. Or is it?
There's Chelsea to beat Newcastle at 1.15 and Liverpool to beat Fulham at 1.20, but frankly the payouts are... poor.
$50 on Chelsea (-2.5) vs Newcastle (at 2.60) - Yes, that's -2.5, not -1.5. Sad to say, the Blues probably can do it
$25 on Man City to draw Arsenal (3.20) - Gallas finally gets the chop. Likely a good move as he never looked real captain material. A draw isn't improbable, my gut says (even more than usual)
$25 on Man Utd (-1.5) vs Aston Villa (2.90) - United have a great recent record against Villa, and seem to be finally hitting form; But so are Villa, and Friedel has been a stumbling block for ages when he was at Blackburn. Eleven straight EPL head-to-head wins says United have the upper hand, though
And back to Economics till United face Villa at one am...
Saturday, Nov 22, 2008 - 04:41 SGT Posted By: Gilbert
With my Health Economics and Game Theory examinations being five days away, I thought I would just blog about my chosen subjects by way of revision. This is after I couldn't resist breaking out Championship Manager 03/04 and guide Brighton to the Premier League and beyond (I stopped at the First Division), and discovered a few things:
Players walk very slowly to the referee in the 2D engine
Brighton's David Lee is a world beater, with Beckhamesque free kick ability (20) coupled with C. Ronaldo's dribbling (in real life, he plays at Conference level now though). Gary Hart isn't half bad either
Nobody predicted Cesc Fabregas' rise back then - he was nabbed from Arsenal's reserves for a mere 240k Euros (probably even less if I had bothered to negotiate). No wunderkid tag for him. Loves to take long shots in the game
Ben Foster could be gotten for free from Stoke City
Steve Guppy (35 years old then) wanted 10k+ Euros a week coming from Celtic, and stated he "had no interest in joining Brighton" even for over 3k a week (all I could afford then), whom were then flying high in the Second Division. He proceeded to sign for Northwich Victoria F.C. in a lower division on 700 Euros a week, before eventually being flogged off to Brighton for some 20k Euros and a 1.9k Euro per week salary. Career financial planning seemingly isn't CM4's strong suit
Woodlands would demand over 1 million Euros each for Itimi Dickson and Agu Casmir
Noh Alam Shah would be available for 300k+ Euros, but wouldn't get a work permit
In other news, Football Manager 2009 (the continuation of the series after naming rights were lost, it's complicated) has just been released, with a 3D match engine. In a way this is kind of overdue since all they had to do was plug in some long-available 3D capabilities ala the FIFA XX series, but they've done it decently enough:
So that's that for football manager simulations, on to the main topic: I'll try to collect my thoughts on Economics in general, and Health Economics in particular now, and express them in narrative. Any errors are, of course, my own.
Firstly, the fundamental tenet of all economics is scarcity; If we could have all we desired at the snap of a finger, there would be no need for this field of study. As this is not the case, there is room to explore how to employ our limited resources to produce selected goods and services, for the greatest good (N.B. what is the greatest good?). Here I must add that a lot depends on the assumptions taken, and in actual fact I am uncertain of how accurate some of these assumptions are. Many times a problem is posed with some mathematical function modelling for the utility of a population, and thus the "correct answer" can then be dragged out from the given figures with some manipulation.
In reality, I feel that the precision of the function, and if it is even appropriate to consider a problem by a certain method at all, is probably the major part of economic skill, as the math is relatively trivial once the assumptions are made. It appears there must be some limitation to the degree of perfection that economics can attain, as there exist non-verifiable entities (e.g. comparism of utility between two different individuals, or even the true utility of an individual).
[An aside: Saying that the Sun rotates around the Earth may agree with available evidence, but that does not make it true - A person may buy stock X because of reason Y, and if the price of stock X does rise he may infer that he was correct and it was due to Y, but in actual fact it may be due to some other reason Z. The danger in this is that the person may then be misled to be overconfident in his flawed logic, and overextend himself based on it.
One way to distinguish between skill and luck is through repeatability - if a person consistently picks winning stocks 60% of the time, day after day, we then say he has skill, statistically. An interesting question then concerns those who take huge one-off risks and succeed (e.g. walking into a casino and putting one's life savings on a single number at the roulette table, and winning) - can we call that skill? One might say that is clearly luck, but surely few long-term gamblers can ever claim a 3500% return, and it is the practical result that we are after, no? In other words, does it even matter whether someone succeeds (or fails) through luck or skill? For more on this, a possible read is Fooled by Randomness by Nassim Taleb.]
Leaving these considerations aside, the basic principles of economics are admittedly a reasonable approximation in some situations (as Newton's physical laws were. Incidentally economics might even be viewed as an offshoot of physics: "...the progenitors of neoclassical economics, all of whom were trained as engineers, developed their theories by substituting economic variables derived from classical economics for physical variables in the equations of a soon-to-be outmoded mid-19th century theory in physics.") - take the Law of Demand, that states that all other things being equal, as the price of a good rises, the quantity demanded by consumers falls (unless the demand is perfectly inelastic, that is, or the good is a Giffen or Veblen good). This is simple enough that it can be recognized as true in general. The corresponding Law of Supply states, what else - as the price of a good rises, the quantity produced by firms will increase. And where Demand meets Supply, we find Equilibrium, and consumers and firms transact and rejoice.
So does this happen in real life? Well, there are many imperfections. Offhand, there are additional costs associated with obtaining market information (e.g. reading the classifieds), adjusting prices (e.g. printing new price tags and adverts), labour practices (e.g. relatively long-term contracts, compensation, retraining, acclimatization etc), and this already for so-called perfectly competitive markets where there are many relatively small firms producing near-identical goods. Exactly how much all these imperfections reduce the applicability of economic theory, and whether they can be offset, should be a worthwhile study. When market power comes in, and a few firms (or one) dominates an industry, more considerations come in.
A timely case study would be the U.S. automobile industry, whose CEOs made the sincere gesture of flying in private jets to Washington to beg for another US$25 billion from the public (though in truth that expenditure is probably among the least of their concerns as cost structures go - they had better come to some sensible agreement with the unions ASAP, and from what I've read it appears that unions in the USA have gone from the admirable goal of protecting the "little guy" to hamstringing operations with dumb rules such as "no picking up your own litter, or you'll be putting the janitor out of a job"). If cast as an examination question, the answer is straightforward - let the inefficient automakers fail. In practice, sheer size has its own distortion field, and as classical mechanics does not apply at extremes, neither does classical economics.
And on to EC3353 Health Economics. The basics of general economics of course apply. The syllabus is as follows:
Week 1: Introduction to USA/UK/Singapore Health systems
Week 7: Non-profit Firms/Hospitals and Long-Term Care
Week 8/9: Pharmaceuticals/Technological Change
Week 10/11: Managed Care (apply Adverse Selection)
Week 12/13: Government Health Insurance/Health System Reform/Comparative Health Care (+Canada/Japan)
Week 14: Epidemics/Addiction
I will attempt to summarize the key points below (click button to display, since I didn't want to overload my blog):
Week 1: Introduction to USA/UK/Singapore Health systems
"Your true value depends entirely on what you are compared with" - Bob Wells
Health care often involves a third party, unlike some markets, as there is a high and unpredictable variance of spending that opens the door to risk mitigation (more later). It is also special in that many may feel that it is an entitlement (especially when the health defect is inborn/unavoidable).
Different countries have different approaches to health care. The USA has a universal system called Medicare for all citizens over 65 years old, which is a collective "pay-as-you-go" fund to which workers make a fixed percentage-of-salary contribution (the demographic shift of the USA, and technology [more later], presents a financial time bomb this way, though). Medicaid is available for the needy. Those who are in neither category usually have employer plans (that are lost if they leave the firm or the firm goes bust), or go uninsured. Health care takes up over 15% of GDP (in 2003)
The United Kingdom has a National Health Service that covers everyone, and they own most medical facilities and employ most medical staff. In this way, they sidestep the problems of private insurance (more later). The flip side is the higher taxes to fund the system, long waiting times, and lack of incentive (since doctors are paid a fixed salary or by number of patients, and hospitals get a fixed budget). A possible philosophical concern is whether it is right for a state to enforce what is effectively the subsidy of people with poor health (which may partly be their own fault) by the healthy. N.B. A couple of weeks ago, they began paying people to lose weight... Health care is about 8% of GDP.
Singapore has upheld individual responsibility with Medisave, which may be augmented with Medishield, with Medifund as the safety net of last resort for those without other means to pay (the 3Ms). 80% of hospital beds are private, while 80% of primary care is by private doctors. Health care is just 4-5% of GDP.
Examination comments: Some memorization of facts to begin with
"I suppose that I shall have to die beyond my means" - Oscar Wilde
Markets may not be economically efficient when there are externalities (an entity's actions affect others as well - may be positive as with streetlights outside a private home, or negative as with secondhand smoke) or asymmetric information (where one party knows more than another). In these cases, another agency (often the government) might then step in and calculate the costs and benefits to determine if they should take up the responsibility. Again, making good assumptions for these values is an art in itself, since with the right values you can draw whatever conclusion you want. Practice examples usually involve two jobs where all other factors other than mortality risk are equal, and thus in theory the willingness to pay for a statistical life is just the difference in pay between the two jobs (normalized for working population size) divided by (normalized) difference in lives lost. In general CBA involves discounted present value (i.e. payments later are worth less than payments now due to interest rate [Question: How to assume fixed interest rate in reality? Government bonds?] - covered in Financial Economics).
Introduces the Standard Gamble method (partly invented by a pioneer of Computer Science, John von Neumann) of measuring preferences, which is just comparing a "guaranteed" outcome (e.g. living on with an inconvenient disease) to a gamble (e.g. going for an operation to cure that disease, but which has a small chance of death). Used with Quality-Adjusted Life Years, which just assigns a value from zero (equivalent to death) to one (perfect health) to each year of life. N.B. As minimum quality of life is associated with death, under this system there is no call for euthanasia (as recently appeared in the news). In reality an extension to negative quality of life is probably not impossible under certain unhappy conditions (e.g. incurable intense pain).
Examination comments: Can add, subtract, multiply, divide, take the exponential? Good to go. Just keep in mind what to compare with what (especially with WTP for statistical life)
Week 3: Production and Demand for Health (Capital)
"Quit worrying about your health. It'll go away" - Robert Orben
Health like almost all goods is subject to diminishing returns (e.g. visiting the doctor ten times a day is probably not that much better than once). Historically, declines in mortality [McKeown, Fuchs] were mostly due to preventive measures: availability of clean water and better nutrition, improved environments (think smokestacks of old), and basic public health (mass vaccinations) - thus the "epidemiological transition" (big word!), as infectious (air/waterborne) diseases became less widespread. Curative medicine, or fixing diseases only after they appear, was the least important (and most expensive) factor. Indeed mortality nowadays is dependant on health care spending, but it takes relatively high spending for small differences [Hadley, 1982]. Smoking/drinking has a weak negative effect (see also Utah vs Nevada example), educational levels some positive effect, and income next to no effect (!)
The RAND study [1970s] is a rare controlled trial in the social sciences (bankrolled by the US government) which provided randomly selected participants with different levels of health insurance co-insurance (i.e. at a 95% rate, the insurance company pays 95% of any treatment while the insured foots the remaining 5%, of which more later). Findings indicate reduced spending by those who had to foot more of their own bills, but no significant mortality differences between the groups for most people, implying that low levels of co-insurance lead to overusage of health services. N.B. Example dissenting argument as counterbalance. [Bunker, Frazier, Mosteller, 1994?] estimated that current effective medical interventions add about five years of life expectancy (compared to a ~30 year increase over the last century)
People want health and not really health care (which is a derived demand)
Health can be thought of as a form of capital since it lasts over time
Health is valued both for itself [consumption motive] and because it can lead to increased income (e.g. having to take fewer days off work) [investment motive]
Then health capital in a period t+1, Ht+1 = Ht(1 - dt) + It(M,TH) where dt is the depreciation of existing capital in the previous period (an outflow) while It(M,TH) is the additional investment in health capital in the previous period, which depends on medical care M and time taken TH. N.B. in this model health capital is determined period-by-period. Then the maximization of consumer welfare B can be found, if the function of B as a consequence of other purchases (not health care), time spent on leisure, and health capital H is known (since H reduces time lost to illness, the time saved can be allocated to work for more income [investment motive] or leisure [consumption motive? or should there be a H multiplier]).
N.B. health capital is constant when Ht(dt) = It(M,TH), i.e. investment each period balances the depreciation. A one-off change in either dt or It should lead to a new stable equilibrium level of health capital eventually. Computations will probably get unnecessarily tedious with varying dt, and I doubt such questions will appear.
Graphical analysis for any single period consists of a downwards sloping marginal benefit per unit curve (MEI) against a horizontal (constant) cost per unit curve. Cost is represented as C(w,p)[r+dt], where w is wages (which raises the implicit cost of spending time on healthcare rather than working) and p is the explicit cost of healthcare. r is the interest rate (since money not invested into health capital could have earned interest sitting in a bank). Essentially, the true cost of a unit of health capital is usually much lower than the full cost of production (as r+dt should be relatively small), as most of the capital produced is not used up, but continues into future periods. Observe then if r is effectively zero (seems to be the reality these days) and dt is very low, then health capital is effectively free - probably the model assumes a certain inborn level of health capital at birth (t=0).
Then from this model, since in general the MEI of older individuals is lower (as they expect a shorter time to enjoy their health capital, and do not forego income through poor health if retired), and the marginal cost is higher (since health capital depreciates more quickly for them), it can be predicted that older people should aim to reduce their stock of health capital relative to their youth. This meshes with the real-life observation that old people seem to spend more on health, because their increased spending does not maintain their original high level of health capital due to their higher depreciation rate.
Examination comments: Revise dynamics of variable changes for the Grossman model.
"Scientia potentia est (For also knowledge itself is power)" - Sir Francis Bacon
Benefits of insurance are not limited to health of course, and arise due to the diminishing marginal utility of money - the intuition is that the happiness of getting a salary of $30000 instead of $20000 does not offset the sadness of getting only $10000 instead of $20000, or in other words an extra dollar is much more valuable to the poor than the rich. Thus most people are risk averse in that they would much prefer, say, a guaranteed $1 million instead of a 50% chance of winning $2 million and a 50% chance of nothing, despite the expected value of both offers being equal. Indeed it would be understandable if someone took $100k and ran, instead of going for a 50% chance of $2 million.
The general idea behind insurance is that the overall losses for large numbers of people are predictable, especially if the occurance of losses is independent (perhaps not so in cases of epidemics, or large fires for property insurance, but I guess the statisticians at insurance companies know how to cover their backsides). Then firms can take advantage of these facts by collecting premiums from a lot of people, using some of these collected premiums to compensate those who randomly suffered losses, and keeping the rest as operating expenses/profits. The individuals also gain since they now have a higher expected utility, since even if their expected wealth may be reduced, the reduction in risk more than makes up for that. What's not to like?
A few problems: Major problem one is moral hazard - let us say that a person's bicycle is fully insured against loss, by a firm that observes that a bicycle has a 1% chance of being stolen each year. Now, that person has a much lower incentive to be careful about taking care of his bicycle, such as bothering to lock it, since he gets a new bicycle if it gets stolen anyhow. Unsurprisingly the number of claims will be higher than the original estimation, and the insurance firm suffers losses from the increased payouts.
The solution is then to shift some of the pain of losses back to the insured. One way is through co-insurance (remember the RAND study from Week 2?), where the insurance company pays only an agreed percentage of the total loss. Then, the insured is more likely to take more responsibility to prevent losses (such as exercising more, in the domain of health care), if still not as much as when he did not have any insurance. Of course, part of the original welfare gains from risk elimination through full insurance are now lost. The optimal level of co-insurance can then be computed as a balance between these two considerations, again given the appropriate functions.
Other restrictions available to insurers are deductibles (the insured can't claim anything for small losses), limitations (e.g. maximum payouts or stop-loss, which cap the risk to the insurer), and of course adjustable premiums (which aren't specifically mentioned in the notes - perhaps not as applicable to health as opposed to say auto insurance?)
Major problem two is asymmetric information (also heavily covered in Money and Banking I) - here's where the knowledge is power thing applies. Consider a world where both individuals and firms know the exact risks of getting ill for each individual - then firms would just tailor a policy to each individual depending on his risk level, and both sides gain from this agreement as explained above. Now consider a world where both individuals and firms know next to nothing about individual risks. No problem, if the aggregate risk of large numbers of people are known - firms just offer policies catered to the average risk, and since individuals have no idea of their own susceptibility to disease they have no reason to decline coverage.
Trouble comes when one side knows something the other doesn't - in reality, individuals likely know more about their own medical conditions/potential than insurance firms. True, firms usually ask individuals to disclose some information (with penalties for lying, if discovered), but this probably doesn't cover everything. Remember that insurers who do not have distinguishing information must base their premiums on the average risk (if they base premiums on lower risks, they take losses) - but the following argument applies for any premium other than that based the very highest risk.
Now, some of those who would be insured would recognize that they have lower risk than the average and thus are overpaying (remember, they have information about themselves), and therefore drop out or not sign up for the policy. The rest would be willing to stay since they benefit from underpaying as they have a higher risk than the average. Unfortunately the loss of the first group of people raises the average risk, and thus the premium, and the same situation occurs where the ones who are now overpaying drop out, until only a very small group with the highest risks remain - the rest go uninsured since they do not want to effectively subsidize those with poorer health.
If the influence of asymmetric information is strong enough, the only viable solution then might be for the government to regulate or simply take over health insurance and make it compulsory (see the UK system), thus preventing the low risks from dropping out (and have them subsidize the high risks). Whether that is fair is another matter altogether, but it certainly makes things rather simpler.
Bonus trivia (outside of the module): The most important form of insurance a young person should take is probably disability insurance. Look at it this way - for most other accidents, one can at least work to cover the losses, but disability can be a drain that a family cannot recover from. It is probably possible to be badly overinsured as well - for example, an older person with no dependants or liabilities remaining has little need of life insurance.
Examination comments: Possibly questions based on market failure due to asymmetric information, e.g. double coverage. Just go through systematic analysis
Week 6: Physician's Practice/Services
"Doctors are men who prescribe medicines of which they know little, to cure diseases of which they know less, in human beings of whom they know nothing" - Voltaire
Private doctors likely operate under monopolistic competition as there are certain differences between their ability and availability. Asymmetric information also exists here, as when illness actually strikes, the doctor generally knows more about how best to treat it than their patient (which is why they are approached by patients in the first place). Relying on the seller for advice is understandably not regarded as very smart in most markets, but it appears unavoidable (at least without burdening overloaded health systems further) in medicine (with private doctors at least - government/managed care plan-employed [more later] ones on a fixed salary have less incentive to prescribe more profitable treatment, but it cuts both ways). This effect is somewhat mitigated by the doctors' reputation.
Personal thoughts: While obviously doctors are as a whole professional and ethical, it is hard to imagine them being completely unmotivated by financial concerns. Take for instance a new drug that he thinks is slightly better than the alternative, but is quite a bit more expensive (and thus brings say twice the profit margins). Should a doctor switch to prescribing it, or should he discuss the pros and cons with a patient (do they even do that most of the time?). Note that the drug example is only applicable for countries where clinics have attached pharmacies (like Singapore). A more general example would be follow-up care - it may indeed be in a patient's best interests to visit (and pay) a doctor now and again, but how often? This is known as Supplier-Induced Demand (SID).
There also exist variations in medical practice (aka Small-Area Variations) where doctors in different areas tend to have their own styles and diagnoses, perhaps due to habits from different medical schools. This clearly causes inefficiencies either from too much or too little care provided, and might be reduced through standardized guidelines and protocols (including computerized expert systems?)
Another issue is the number of doctors - can there be too many of them? Economically yes, but this is probably not the case yet for most countries. Given limited resources, it is often good to ask if some medical slack can be taken up by other professionals, such as trained nurses and midwives, however. Other barriers to entry include limited intakes for medical schools (true in Singapore). Possibly of concern is the fact that much of the regulation is by doctors themselves, which is probably a factor in practices like undisclosed fees (which may prevent doctors from going down the undignified route of price-slashing to get business, but also makes it possible to overcharge richer patients for specialized services since no easy comparisms can be made, and the service is non-transferable. A common example problem concerns two groups of patients [rich/poor] with different demand curves)
Examination comments: Practice examples on price discrimination
Week 7: Non-profit Firms/Hospitals and Long-Term Care
"Health nuts are going to feel stupid someday, lying in hospitals dying of nothing" - Redd Foxx
Considering the hospital as a normal firm, the standard concepts of technical and allocative efficiency, economies of scale, cost minimization etc all apply. Non-profit hospitals, where no residual claimants of profits are allowed (as opposed to doctor-owned hospitals, which are popular in Japan), also exist (similar situation to UK government funded ones). However a zero-profit constraint may still allow hospital managers to favour quality over quantity due to prestige factors [Newhouse], resulting in inefficiency from underutilization of advanced technology ("Medical Arms Race", which can be modelled as a game theory problem). For doctor-owned hospitals, the decision on whether to admit new doctors (partners) may hinge on how much extra revenue he can bring in, compared to his cut of the profits. Also depends on capital equipment and salaries of other staff. Of course, altruistic motives may also play a part (though they usually aren't modelled in given problems).
Examination comments: Mostly the usual analysis of firms
Week 8/9: Pharmaceuticals/Technological Change
"[Medicine is] a collection of uncertain prescriptions the results of which, taken collectively, are more fatal than useful to mankind" - Napoleon Bonaparte
Pharmaceuticals (more commonly medicine/drugs) generally make up 10-20% of treatment costs in developed countries, more in developing ones (e.g. over 50% in China). They have the property of being very difficult and costly to discover through research and to trial for safety purposes, but very cheap to produce after that (possibly by reverse engineering).
From the viewpoint of society, it is efficient for the drug to be sold at the (low) production price, but this cannot happen (at least for some years) if pharmaceutical companies are to get profits (and thus continue developing new drugs). Thus the patent system (which does apply to many other forms of innovation) is employed to allow companies to sell the drugs at a high price (to patients who have little choice but to pay up). Usual balancing act of the length of the patent (now ~20 years) applies - too long and society is denied full use of the drug for even more years, too short and companies are not adequately rewarded for their innovation (as other firms can produce an identical generic version), and may hinder new investment and discoveries. The scope of patents also matter - too broad and minor improvements are not recognized, too narrow and other firms can just tweak the formula a bit and claim it as their own. Same goes for the comprehensiveness of testing.
Internationally, the patent system (usually national) has sometimes been ignored by countries without much ongoing research & development, as they just produce the patented drugs anyway (free-riding/piracy - see Brazil). Clearly this act saves lives as poorer patients now can access the drugs at an affordable price, but is unsustainable if too many do it. Personal comment: There might not be a big loss for the companies if the demand for their drug at the original (high) price is very low in those (probably poorer) countries to begin with. Of course, if significant amounts of generic/pirated drugs get exported, they will be badly hit (possible for Singapore/Malaysia, as with groceries?).
The Goddeeris model (remember spelling) asserts that new health-improving technologies (e.g. a new cancer drug) are effectively subsidized by insurance, as opposed to cost-reducing technologies that may be used by doctors and hospitals (e.g. a cheaper X-ray machine). Thus inventors of the former can charge far more, since doctors can charge their insured patients more for usage.
Finally, one dimension of technology is that it often allows us to prolong life - at a price. I forget where I read that "there exist treatments that are able to keep patients alive but with little quality of life, and reduce the rest of the population to penury" (and everybody dies in the end), but that sums up the issue well enough.
Examination comments: Study the Goddeeris model, especially the graphical representation
Week 10/11: Managed Care (apply Adverse Selection)
"Be careful about reading health books. You may die of a misprint" - Mark Twain
Managed care (MC) was mentioned as a solution to the moral hazard problem of insurance. It essentially locks patients into getting chosen treatments at selected providers, and since doctors assigned by the insurance (managed care) firm do the diagnosis, there is no concern at the patient buying too much of healthcare services, just because they are subsidized. Of course, this implies a higher level of trust placed with the insurance firm, as they have an incentive to drive away riskier (and therefore more expensive) consumers [Dumping], try to attract fitter ones [Creaming - Prof: perhaps by having one's offices on the 20th floor of a building without an elevator?] and underspend on treating insured people [Skimming], counterbalanced by reputational concerns. Again very similar to UK model with gatekeeping, capitation, etc
In practice, costs for Health Maintenance Organizations (strict form of MC) do appear to be lower, a good choice for healthier people, and they support more preventive care since they lose out on expensive curative treatments. Less strict forms of MC are Point of Service (POS), which allows out-of-plan providers, and Preferred Provider Organizations (PPO), which offers discounts on affiliated providers. Providers such as hospitals and doctors may not like MC much, but will agree to get the patients on MC plans ("patient steering")
Introduction of normative considerations (what should be, versus positive's what is) - two main concerns, of efficiency and equity. Note MC cannot overcome adverse selection.
Examination comments: Seems mostly understanding only... study adverse selection example for HMO vs FFS
Week 12/13: Government Health Insurance/Health System Reform/Comparative Health Care (+Canada/Japan)
"A government that robs Peter to pay Paul can always depend on the support of Paul" - George Bernard Shaw
Can't opt out into private insurance in Canada and Japan, their "public contract" systems are funded through taxation, but unlike the UK the government does not operate the providers as well (mostly private in Canada, a mix in Japan). Outpatient care paid through fee-for-service (FFS), hospital budgets often negotiated in Canada. Relatively low costs in Japan due to fees being biased against hospitalization, but expensive drugs (coincidentally supplied by doctors, like in Singapore). However long waiting times (appears a feature of collectivized plans)
Interesting development - voucher models (inspired by Alain Enthoven) where the government provides a voucher to citizens, who can then use it as partial payment for a private insurance plan. Attempts to achieve near universal coverage and reduce adverse selection, featured in Clinton's plan (1990s) and the Dekker-Simmons plan in Holland (2006). See Obama's plan. This model appears to be gaining popularity.
Examination comments: Back to memory work
Week 14: Epidemics/Addiction
"Every form of addiction is bad, no matter whether the narcotic be alcohol, morphine or idealism" - Carl Jung
Rational addiction model: Choices that have future negative consequences (e.g. smoking) may still be undertaken by rational people if they discount future suffering greatly (i.e. prefer to enjoy now, rather than wait for a tomorrow that might not come). Addiction can then be explained by addiction capital (remember health capital in the Grossman model, week 4?), the idea that the enjoyment derived from an activity (smoking, drinking, classical music, DotA) is dependant on the amount consumed previously ("use it or lose it"). Standard arguments on externalities and government intervention enter - taxes, advertising bans (e.g. tobacco and Formula 1), outright bans (Prohibition didn't go down too well, though).
Epidemics: Not everyone needs to be vaccinated for acceptable results - the costs may be very high for the last few holdouts (whether due to concern about side effects, or religious objections), and the benefits low since most people can't be affected anyway - simple marginal costs/marginal benefits intersection, though determination of marginal benefits not straightforward. External benefits rise initially when most are uninfected, and eventually fall as the chance of meeting an infected person falls due to previous vaccinations.
Examination comments: The two models, not that many details to be bothered about
Saturday, Nov 15, 2008 - 21:34 SGT Posted By: Gilbert
Total Relax
After managing an overdue breakthrough of sorts in my FYP, and tying up more loose ends (including applying for further studies at NUS), I decided to just take a few days off as Reading Week looms again. Broke out the old Simcity 4 and plonked down several cities, breaking past the 100000 population mark with one of them - the big one million probably will take some serious creative destruction.
Gilberta Central
Took the opportunity to spend more time with the hamsters too. Mr. Ham G. Bacon got interrogated for his part in the great escape (refer previous post) by my grandmother, who has years of experience with this business under her belt. A few minutes of tough-guy holding out and defiant squeaks of "I'll never tell!"/"Are you trying to steal the food in my mouth?" soon were all that poor Ham could sustain.
Okay, actually all that my grandmother wanted to know was whether a hamster has two (bottom) teeth, or three. I had internet evidence, but she insisted on the most direct observational evidence:
Two teef or three? You decide
If that distressed you, click on over to the Puppy Live Cam (recommended).
Signing off with the predictions of the week (on $880.75/$1100):
$50 on Man Utd (-2.5) vs Stoke City (at 2.00) - Long odds against the long-throw specialists, but a sneaky feeling they'll storm through this one
$50 on Tottenham to beat Fulham (at 2.10) - A dramatic turnaround of fortunes by Spurs under Redknapp. What a difference a manager makes.
Saturday, Nov 08, 2008 - 20:27 SGT Posted By: Gilbert
(HamWire) Convicted Campbell's hamster Mr. Fish F. Chips, 1, was recovered from under the bottommost shelf at the back of a storeroom behind a heap of items after a 12 hour-long search that involved multiple family members. Chips was promptly given food resuscitation, and returned to jail.
Chips was last seen wrestling with longtime cellmate Mr. Ham G. Bacon on the second storey of their deluxe cell at approximately 4 a.m. on November 8. That was the last that was to be seen of him for over twelve hours, as the dastardly duo staged a prison break between then and 5 a.m., when the rotund Bacon was apprehended by Uncle M after scurrying aimlessly across the living room floor tiles.
Partner in crime Chips was nowhere to be found, though, and the worst was assumed after a comprehensive search of the house was completed. Beds were peered under, cupboards opened and flashlights shone, but to no avail. Grandfather even went on a fruitless search about the void deck, in case the intrepid hamster had taken a fifteen-storey plunge off the balcony. No body was located.
No signs of life were observed either, though advice from the Internet indicated that the species was known for its nocturnal habits, and could very well lay low for days on end. Several searchers concluded that Chips was lost forever after a few hours of their best efforts, and suggested a replacement cellmate for a blissfully ignorant Bacon, who spent much of the intervening time dozing off. Explanations along the lines of Chips having a more magnificent destiny as a wild hamster after floating to the grass unscathed were suggested. Uncle P was one of the few dissenters, and following standard practice, food caches (including peanut butter) were laid out more in hope than anything.
Chips' hideout
Things were looking bleak until Uncle M returned from work and set about the rescue operation methodologically, as befits an engineer. The television cabinet was first to be dismantled, but it was not until something furry was felt huddled in the shadows of the storeroom, was the matter resolved. Chips put up a valiant last stand, having taken a dust bunny hostage, but gave himself up after an offer of three honey stars and a dab of peanut butter.
Chips, back behind bars
The prisoner was returned to his rightful location amidst much rejoicing, whereupon having tasted liberty he embarked upon an energetic spate of wheel-running, in between bouts of attacking Bacon for already having taken possession of his secret stashes in his short absence. The two will continue serving their life sentences, with Chips' additional ten years for his latest transgression to be run concurrently.
Reaction to the breakout has been mixed - while it has caused many to be able to better appreciate life's little pleasures, various hamster freedom fighter groups have hailed Chips as an inspirational hero, and reaffirmed their pledges for "Liberty or Death, or at least four honey stars".
...a written report
Or reaching campus for a meeting with my advisor with not much new to report, and realising that he wasn't free anyway. Figured out some extra stuff about the Torque Game Engine, so I'll probably be able to survive the 10-15 page CA Report to be submitted by Wednesday. Come to think about it, I probably don't need to be concerned overmuch about the page limit, since it's more common to have to slash than to stuff in my experience. A literature review being part of the report helps alot.
More news - Caligari trueSpace 7.6 [127 MB], a 3D modelling/animation package which used to cost upwards of US$800, is now absolutely free of charge (thanks to Microsoft). It's gonna take time to learn humanoid character modelling, but when there's a will, there's a way. MakeHuman [28.6 MB] will probably help in producing the initial body frame, but there are of course multiple ways. I've already tried Blender for an MNO movie, and will probably need its DTS Exporter some time or other.
Of course, I suppose just modelling rigid structures first is much easier, and indeed doing the easy stuff first is the way to go - at least there will be a guaranteed end product.
...Man Utd to beat Arsenal
One can hope. Despite all of Arsenal's troubles, the Fink Tank still gives them a 41% chance of winning outright, as opposed to 35% for United, based on computer modelling. Singapore Pools has United as the favourites at 2.25 for the win, compared to 2.77 for the Gunners though, and they actually put their money where their mouths are.
My unlikely draw trifecta last week nearly materalized, if not for a Roman Pavlyuchenko winner in injury time (again, not that I minded). That still paid out a virtual $236.25 for the best week so far this season, and corrected my overall numbers to a more respectable $880.75/$1000. The selection this week is obvious:
$100 on Man Utd to beat Arsenal (at 2.25)
Thursday, Nov 06, 2008 - 03:42 SGT Posted By: Gilbert
Caught the Singapore run of the musical at the Esplanade Theatre (Circle 2, HH-22) on Tuesday night with fake chong, occ & joseph, and thus will never look at Sesame Street the same way again after a dose of "full frontal puppet nudity".
I again heard another familiar-sounding song that no-one knew the title too before the show began. Argh. At least I recalled one of my life's ambitions, to beat up a Teletubby, on the trip there.
Once again, I didn't manage to find the names of the cast members on the official site, though it seems that most of them are from the Philippines. Maybe the details were in the programme, but since I already owed fifty-five bucks to occ for the ticket, more purchases were not on my mind.
Okay, on to the show proper. General spoilers coming on, but you wouldn't care, would you? The opening numbers, "What Do You Do with a BA in English" (Youtube clip) [or Computer Science/Economics for that matter] and "It Sucks to be Me" (Youtube clip) fairly resonated with me (btw I don't want to talk about my FYP). Tidbit: The real Gary Coleman (if you know him, your American pop culture-fu is strong) supposedly wanted to sue the producers for the inclusion of his character.
Gay issues surfaced between the puppets Rod (i.e. Bert from Sesame Street) and Nicky (i.e. Ernie) in "If You Were Gay" (Youtube video, Harry Potter version). "Purpose" (Youtube video) ["that little thing that lights a fire under your ass"] was okay, nothing too special relatively. "Everyone's A Little Bit Racist" (Youtube video), it's true (but a milestone was passed today on that, on which more later). So just be careful where and to who you tell your must-listen ethnic jokes to.
Then probably the most famous song of the lot: "The Internet Is For Porn" (Youtube clip, Harry Potter version again) [indeed. it seems safe to say that at least close to half the bandwidth of the whole Internet is devoted to, what else, happy people]
"Normal people don't sit at home and look at porn on the Internet!" - Kate Monster, Delusion of the Year Award Winner, probably right up there with Quote #1 and #2
Next up - "I'm Not Wearing Underwear Today", "Special", "You Can Be as Loud as the Hell You Want [When You're Making Love]", "Fantasies Come True", "There's a Fine, Fine Line" and How-to-search-Youtube-for-video-clips-by-yourself.
Twenty minute intermission, then Act Two. After we have "There is Life Outside Your Apartment" and "The More You Ruv Someone", there comes Schadenfreude (Youtube clip - Wikipedia definition) ["When I see how sad you are... it makes me sort of... happyyyyy" - "Happiness at the misfortune of others... that's German!"]
"I Wish I Could Go Back to College" (Youtube clip) [the idea is not to leave in the first place - oh and "to f**k my TA" must have brought back memories for someone :P]
Next: "The Money Song" and "School for Monsters" (go look them up yourself). Despite Trekkie Monster's suddenly revealed riches ["In volatile market, only stable investment is porn!"], it turns out that porn probably isn't recession-proof any longer.
Two songs repeat, then it all closes with "For Now" (Youtube clip). ["George Bush - is only for now!" (more later)] Yup, things are only for now!
In a way it does suck a little to be me, but surely there are people far worse off, though that doesn't (and shouldn't) completely negate that sucky feeling. A little more hope, a little change needed?
Always wondered what the Raffles Museum of Biodiversity Research (at S6) was all about, but never found an excuse to drop by until demanded to by my LSM1301 module. I have to say it's the place to go if you have a thing for dead animals.
There was a landmark Changi Tree before WW2 - supposedly over 20 stories tall, imagine that!
Yep, if staring at dead stuff is your kind of thing, you'll have a wonderful time. Joking aside, the colours on the specimens were quite brilliant, impressive given that some of the specimens date from the 19th century.
This is a lousy photo of a cute reminder not to touch the specimens. Nice, but I would have missed both it and the "No Flash Photography" sign had I been slightly less attentive.
The exhibition closed off with a bunch of dead rats, and due to the influence of my hamsters I managed to find some of the smaller ones rather cute. In fact rats are supposedly friendlier to young kids than hamsters (no biting).
While we're on the subject of animals, here's one of the School of Computing Cats that I took a photo of some time ago:
Still, behind all the Hope and Change and GOBAMA chants, a few interesting things to note:
Despite Obama appearing to win by a landslide (and thus have a solid mandate) with about 349 electoral votes to McCain's 163 (a 68%-32% split), in the popular (actual individual-for-individual) vote his margin was only 53%-47% (the ridiculousness of "normal" democratic implementations being discussed here before).
If you subtract:
Bush and his administration (probably worth ten points by themselves)
The financial meltdown
The ongoing issue of Iraq
Palin
from the equation, it becomes apparent that McCain was running under one heck of a handicap. Some of these problems were self-inflicted or a necessary consequence of the Republican ideology, but if say the subprime bubble hadn't imploded right on schedule in the run-up to the election, and he hadn't scared off undecideds with the possibility of a frighteningly underqualified Vice-President, he might actually have been in with a good shout.
It was the young people (duh) and women (ah) who won it for Obama:
How much change can Obama actually deliver? Remember '92, Gulf War, recession, "Change vs. more of the same" slogan, fresh-faced Democratic challenger? Yeah, that was Clinton, who was not too bad no doubt, but one gets the sense that nothing really changed.
Still, interesting times ahead, and whatever happens Obama couldn't possibly be worse than Bush. Right?
So will a great nation be United again? Stay tuned.
The Laws of the Game aren't rewritten often, but it seems a new rule has been added:
"A direct free kick is awarded to the opposing team if a player commits any of the following offences in a manner considered by the referee to be careless, reckless or using excessive force..."
"...being jumped at by an opponent."
True, everyone's a bit of a hypocrite, but when someone who rails against diving in his autobiography and in the press does his best dying swan impression, I guess he can take some stick for it.
changelog v1.09b
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* New comments, regardless of age of original post, will now trigger an email for Instant Response:
Only a week and a bit left to the Interim Report for the HYP to show what I've done on it so far (hint: not that much), but I think I'll keep my mind off it tonight at least, since there are still five or six months remaining, and my advisor seems to be hinting that the Report is not that important anyway (first batch to kana it. Gah) - I'll just have to bone up on my Desperation Programming feat once the examinations end. I think I'm pretty decent at that, by the way.
So, just in case anybody was wondering what a Computer Science university undergraduate does (other than playing researching computer games), I'll delve a bit into Lab 3 of CS4213 Game Development. Oh wait, that's researching computer games. Never mind. On balance some future student will probably Google this post up, so if you're him/her, hope this helps.
First off, I opened the Word document describing the lab. "Lab III: Neural Networks for Decision Making". Hmm. Next up was several pages mostly describing the classes and methods in the provided skeleton code, which weren't very inviting.
A summary: The lab is about implementing a simple neural network AI for (sixteen) robot enemies in a simple first-person shooter game (so simple that there's only one weapon, and not even any walls). There's Data Collection program code, Neural Network program code and the actual Simulation (game). The idea is to collect data using the Data Collection program, feed this data into the Neural Network program to create a neural network, and have the robots use the neural network to make decisions in the Simulation, and we're done. Ta-dah!
The high-level overview is simple enough, but coding all the nitty-gritty stuff isn't that straightforward. Furthermore, I didn't have any practical experience with neural networks (thereafter NN). The general idea behind NNs (AFAIK) is that they allow, given a selected set of inputs, to predict (certain) outputs. Let's have a simple example with two inputs: Age and educational level, and one output, the probability of getting refunded on a bad investment. Using this, we set up NN with three layers - the input layer, the output layer and a hidden layer (with perhaps two cells [why?]) in between them.
Having defined the structure of the NN, it's time to train it with actual data. Each input is ideally normalized such that it has a minimum value of 0 and a maximum value of 1. So, for age, we can have 0 years old as zero, and 122 years (current record) as 1. For educational level, we can probably work out some scale with no formal education at all as 0, and a terminal degree as 1.
So let's say we encounter Mr. X, a 70 year-old retiree with primary school education, who got his money back. Then, the input data would be something like (0.57,0.2), and the corresponding output data is (1). Next is Mr. Y, a 30 year-old investment banker with an MBA who probably isn't going to get anything back. His data would be (0.25,0.9),(0.01). By feeding all these data into the NN and iterating many times, the weights for the cells in the hidden layer(s) are eventually adjusted such that feeding the exact same data back into the NN corresponds very closely to reality, i.e. the NN is sort of a black-box function that will take (0.57,0.2) as input and give a value that is very close to the actual output of 1 back.
Why is this useful at all? The answer is that the NN allows output to be predicted with a certain level of intelligence for new data. Even given only the two sets of data so far, it wouldn't take much to guess that (0.71,0.15) should have an output closer to one than zero, and the other way around for (0.22,1.0). While this (and the Lab 3 NN) are rather simple examples that a human should have little trouble working out, I suppose NNs really shine when things get complex with dozens of inputs and outputs, which probably can't be adequately expressed with basic rules-based logic (e.g. FSMs).
Now, using only the age and educational level probably will not be enough to successfully determine whether a person gets back his cash all the time, since other factors like proportion of assets invested, evidence of misselling etc will come into play. Now one can of course model all the inputs one can think of (such as the last digit of the person's NRIC), but many will obviously be of minor or no consequence to the decision and only serve as unwanted noise. Thus, a balance is required - another win for Common Sense.
The next step was then to peruse the module's online forum on the IVLE, to get up to date on any time-wasting bugs, receive other students' insights so far (i.e. learning through others' experiences) and get a general idea of how to proceed. One of the few benefits of starting a lab assignment late.
Data Collection to a text file wasn't too hard - just dump S sets of L lines, where S is the number of samples taken and L = I+O, where I is the number of chosen inputs and O the number of required outputs respectively. I chose I = 4 and since robots have three available actions (Idle, Flee and Attack), O = 3.
Now on to the NN code. Reading the data in from the previous phase wasn't hard, and running the NN was easy too. Then the first major hitch struck. The actual NN structure (complete with weights, biases etc) had to be exported out to a file, to be read in by the Simulation code. The NeuralStructure class is constructed by incrementally adding new Layers, and there was no provision for injecting attributes directly within them (instead of building those attributes through training). I wasted a good few hours trying to serialize the object (the cheapskate way), though I should have gotten the hint that nested objects don't serialize easily (yes, sometimes C++ makes me want to bash my head against the wall). I ended up just adding new constructors that take in saved data in array form, which wasn't quite that hard since the values have a fixed structure behind them.
Finally, the Simulation program itself. I loaded the NN within the RobotManager instance and just had each Robot send their current input values to it every so often. They would then get back output values for the Idle, Flee and Attack actions, and perform whichever was the highest. I daresay even this very simple implementation shows a flicker of intelligence - see below video for example (using a NN which has the robots pursue and attack if close enough, and flee once their health is low enough compared to the player's). Note that in the group battle at 0:40, a robot flees once it is hurt sufficiently, but turns back to give support fire once the player switches his attack target - without this behaviour being explicitly specified!
Okay, in this application a few lines of logic would probably have performed just as well, but that takes all the fun away, doesn't it?
In the end, this lab took the better part of two days, with a big chunk of time sucked up by the ill-fated serialization attempt. So, moral of the story is, just get your head down and code, and things won't be too bad. Chins up!
More random stuff: My cousin gave me an overgrip for my tennis racket. It truly feels non-slip now as compared to the original smooth one, though the handle's become a teeny bit too fat for my liking. Also found a Buddhist intro-book, I Wonder Why, by Thubten Chodron (an American nun, and History major) lying around. A sign that it's time to branch out and widen my range of exploration (and likely critique)?
Saturday, Nov 01, 2008 - 21:17 SGT Posted By: Gilbert
Got a few lingering tasks done today - did the sole Econs tutorial released so far, cleared up some more legacy issues from the summer job, booked my IPPT (ulp) for January, started reading up for the Game Development Lab 3 etc...
The last (all-MCQ) midterm was returned, and on this one I got a rather average score. Some I could put down to not having gone through the notes ("top of ivory tower syndrome"), but getting the income and substitution effects confused was something I would have kicked myself over, had I been flexible enough. They were introduced in junior college, for beep's sake!
Looking at the big picture, I probably shouldn't even be caring about these bits of carelessness; The main concern should be how dumb I am, all things considered. Doing pretty well in Economics as far as grades go is one thing, but then it's all been down to recycling a few key concepts. In the end, pretty much all I did was some combination of solving (admittedly sometimes tedious) simultaneous equations, performing basic differentiation, and applying Bayesian (read: common-sense) probabilities across most of my Economics modules, with some domain knowledge linking it all together. Nothing special at all.
Worse, It'll probably be more of the same inadequacy in grad school. Cue old joke about mathematicians faced with canned food on a desert island beginning "First, assume a can opener..." (Source: PhD Comics)
Some proofs in Game Theory were quite satisfying - I wouldn't have realised that first-price and second-price auctions differed so much in their theoretical underpinnings, though they do converge in cases where there is a large number of bidders (for one particular first-price equilibrium at least - the rigorous and complete derivation appears out of the scope of this module).
Still, my speed at solving such questions isn't particularly impressive, and I'm ashamed to say that even moderately complex simultaneous equations are potentially draining for me - often, after a few steps in, my mind would be wandering onto what I could be doing instead (like conquering the world in Civ 4 on epic speed at gigantic map size). Oh, for that wonderful technical ability to be able to look at abstract symbols and manipulate them effortlessly!
Then again, the history of science occasionally appears weird to me. For instance, algebra and counting numbers have been around for easily thousands of years, but a systematic study of probability came into being only about five hundred years ago. While it is difficult to believe that the ancients did not have an intuition about chance, it seems that none of them managed to relate it to fractions, or thought of them multiplying (i.e. an army is less likely to attack when it is raining, and less likely to attack when it is weak. The enemy army is weaker, and it is raining, so...) in any formal way. Indeed it is well known that Pascal introduced the notion of expected value (which by the way is sufficient to get through a lot of economical toy problems) only in the 1650s, thanks to a gambler friend.
I suppose since proving a known result is almost always much easier than getting the result in the first place (related: P=NP), what seems so obvious from being commonly taught nowadays, might have taken a quite superhuman leap of intellect to originate. Imagination >>> Knowledge.
Apart from this, there are other bothersome issues, chief among the non-FYP related ones being that of the hamsters. I thought that we were all best buddies after one of them presumably felt comfortable enough to relieve himself in my hand, but recently they have come to arbitrarily reject sunflower seeds again. It seems my post as official hamster food delivery guy has come up for grabs, but no fear:
The fate of the civilized world will be determined in three days by the good people of America, but as I have a more important consideration in my FYP I regret that I will have to give it a miss. It would be entertaining if McCain scrapes out a come-from-behind victory, but the thought of Palin as Most Powerful Human on Earth in the not-improbable event that McCain passes on while in office is equal parts scary and hilarious. While we're at it, why not get Paris Hilton on the ticket too?
Eked out a positive return on last week's play-predictions with Sunderland doing it over Newcastle (now up to $644.50/$900). Spurs incredibly came from 4-2 down in the last few minutes to consign Arsenal to a "4-4 defeat", which pulled Redknapp another few notches up in my estimation. Hull are somehow 12/1 outsiders to beat United despite being on top of them in the league table, with United again being quoted a 2.5 goal handicap. Singapore Pools must know that there are a lot of Man Utd fans/brandname consumers out there.
Nothing especially exciting this week, and I don't feel like going with the usual Big Four wins, so I might as well let loose on some draws:
$50 on Middlesbrough to draw West Ham (at 3.15)
$25 on West Brom to draw Blackburn (3.15)
$25 on Tottenham to draw Liverpool (3.20)
(Source: CNN)
