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Saturday, Oct 04, 2008 - 22:48 SGT
Posted By: Gilbert

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"...Bullshit test..."

- Overheard after a certain midterm while the prof was collecting the papers, and probably within earshot. That's honesty for you

More Economics

Well, it was coming. Friday's Straits Times front page headline was "Marketing of risky (structured) products under review - MAS wants complex investments explained more clearly to public". Personally, I think one thing should be mandated to be in big bold letters right at the top of any factsheet or brochure for such products - the minimum guaranteed return (if any). Stating the distribution of risk (e.g. 50% chance of a 10% or better return, 80% chance to at least break even etc) with regards to the future is probably out of the question, unfortunately, unless the banks all submit to an external neutral agency for such evaluations - the accuracy of probabilities usually cannot be debated on hindsight, as the following joke (appropriately referencing the skyrocketing of petrol prices these days) illustrates:

Unhappy at the recent hikes in petrol prices, a man was nevertheless delighted to discover a petrol station that advertised free sex with each fill-up. Every morning, he would make it a point to visit the station on the way to work, with a carpooling colleague in tow.

Each day, after the man paid for his petrol, the station owner would ask him to guess a number between one and ten to win free sex, and each day the man tried but failed:

"Hmm... I'll try 8 today." the man said.

"Sorry, but the number I was thinking of was 7. Better luck next time." the owner replied.

As they drove off for the umpteenth time, the colleague turned to the man and said, "We've been trying almost every day for months, and you haven't won even once. I think the owner's cheating."

The man replied, "Nah, can't be. My wife won twice just last week."

It might be interesting to evaluate the financial intelligence of the average consumer - quick, if one puts $100000 in a three-month fixed deposit that pays 0.4%, what's the interest obtained? $100, though some may answer $400 (and not wholly without reason). By the way, the standard local fixed deposit interest rate seems to be hovering around 1% these days, while inflation exceeds 6% - making the half-life of money about 13-odd years. The universal tax strikes again.

It seems a good idea to duck out the impending recession as an academic for a few more years, tooling about with theoretical models. Not that the university is distinctly non-commercial either, judging from the stalls that spring up at the Central Forum every so often. I was handed an ad for Tatarah.com.sg a few days ago, which re-alerted me to their special bidding model that made some waves when they first appeared. (I also committed another error when I bought a can of Milo not noticing that the Milo truck was parked some twenty metres away, but that's another story)

Essentially, their highest unique bid auction model sets a maximum price for an item, then allows participants to bid any amount equal to or lower than that. The highest bid that is bid by a single person wins. However, since the maximum price is set to a small fraction of the actual value of the item, the eventual winner effectively gets a whopping discount. How then does the seller/auctioneer profit?

The catch (there's always one!) is that putting in a bid also costs money. Take for example a Sony Playstation 3 with a retail price of $599, and a maximum bidding price of $99 (actual example from the website). The "processing fee" for each bid was set at $3. Thus, to a participant, putting in a bid essentially involves paying $3 for a chance to get something worth $599 for at most $99. Note that the processing fee imposes an upper limit on the number of bids a rational participant can make - in the above example, there is no point in putting 200 or more bids, since that would already cost $600 and the participant could just directly buy the Playstation instead.

The exact number of bids that a rational participant should put is probably somewhat smaller, and depends on his belief of his chances of winning. For instance, if he thinks that putting 10 bids would give him a 30% chance of winning, he would go for it - the expected cost is a maximum of $30 + $99 = $129, while the expected return is $599 * 0.3 = $179.70. However, while it is true that putting in more bids strictly raises one's chances of winning, by exactly how much is mostly unknowable, especially since the total number of bids is not shown.

For the seller/auctioneer, he doesn't really care how participants bid - his foremost concern would then be the quantity of bids. In the above example, once he gets 200 bids of any kind, he has already recouped the loss from flogging off the Playstation at a huge discount, from the processing fees alone (in reality the number of bids required would probably be slightly less than 200, as the winning bid will likely still be at the high end of the price range). Note that this is directly counter to the interests of participants, who would desire fewer total bids so they have a higher chance of actually winning!

The next question is, is there a strategy for bidding? Let us first assume that the total number of bids is fixed and known, and each participant is allowed a single bid. Then in the (unrealistic) case where one is the only allowed bidder, the optimal bid is a single cent, which would definitely win anyway. Extending to two, both participants should bid the maximum allowed price ASAP (since in the event of a tie, the earliest bidder wins). This assumes of course that the processing fee (P) and maximum price (M) are relatively low enough compared to the actual value (V) of the item, more specifically V > 2P + M, which should be true. (N.B. Why not both try their luck at a single cent instead of the maximum allowed bid? For much the same reason as the Prisoner's Dilemma)

Things start to get messy with three participants. Now, fastest finger first is no longer a given, since if all three would bid the maximum allowed, any one of them would do better by bailing out to a lower bid. There is technically at least one (asymmetrical) pure strategy Nash equilibrium (i.e. none of the participants can improve their position by changing bids) when two of the participants put in the maximum bid and the last one puts in a bid a single cent less, but this does not say anything about who the winning third participant should be.

To demonstrate a mixed strategy solution (which is guaranteed to exist under certain conditions), let us allow each of the three participants (P1, P2 and P3) only three distinct strategies - S1 (bid $98.98), S2 (bid $98.99) and S3 (bid $99.00), and to simplify the math further assume that the participants consider the cost of the three strategies to be the same (hey, what's two cents?). The processing fee is a sunk cost and likewise ignored. Normalize the payout of getting the Playstation to a value of 1, and assume that participants have an equal chance of being the first to bid. Then the outcome for participant 1 for each strategy is as follows:

A mixed strategy here is some (c1,c2,c3), where cn is the probability of playing strategy Sn (and thus c1+c2+c3 = 1). A mixed strategy Nash equilibrium would then be some (c1*,c2*,c3*) which, if chosen by two of the participants, cannot be defeated in general by some other mixed strategy by the third and last participant.

A counterexample: Consider the mixed strategy (0,0,1), i.e. the pure strategy S3 (bid $99.00). Can this be a Nash equilibrium? The answer is no, because consider if the third participant switches to (0,1,0) - then his expected return rises from a mere one-third to the maximum possible of one. There are many ways of arriving at a mixed-strategy NE, but for this example I resorted to brute force computation and arrived at (0.25, 0.25, 0.50) or thereabouts. Intuitively, this should be about right since playing S1 or S2 gives 2 chances (out of 9) to win outright from the above tables, while S3 gives 4 chances.

Then, if each participant is restricted to a single bid and the number of participants is known, an optimal mixed strategy can be determined by an extension of this idea. Unfortunately, this analysis is probably not very useful/applicable to actual Tatarah auctions (and others of the ilk) for several reasons:
  1. The number of participants is unknown. (An estimate could perhaps be made from past auction histories if released, but this unequivocally increases uncertainty)
  2. Once a sufficient number of bids are involved, any new bid will have a negative expected value (closely related to above point)
  3. Participants can submit more than one bid, which introduces additional considerations
  4. Participants probably don't follow true rationality, which matters

There is a way to reconcile the conflict between auctioneer and participants, though. Instead of a closing time for the auction, which has the risk of not collecting sufficient bids (and thus processing fees) for the auctioneer, the auctioneer can declare a required number of total bids to close the auction instead. For the above Playstation example, it could perhaps be 250 bids - this would guarantee the auctioneer $750 in processing fees, which would cover the retail cost of the Playstation and more.

Participants would benefit by knowing the probabilities involved (though they would no longer be able to get lucky by joining an auction with very few participants. It must be said that this is unlikely to happen often, since the auctioneer would go bust). Refunds for the processing fee, if participants get tired of slow-moving auctions, would probably have to be implemented, but at least in this case participants no longer have an incentive not to publicize the auction.

But doesn't this look like a... lottery? Well, it depends - according to the United Kingdom's Gambling Commission, unique bid auctions aren't lotteries if they "exercise skill or judgement" (like darts in the UK), and "...Examples of factors that may enable operators of reverse auctions to ensure they are compliant include time limits for the submission of bids, the provision of information to participants about previous winning bids (for similar items) and updates on the status of their current bid(s). Operating reverse auctions of this type may make it possible for participants to apply a strategy to their bidding (demonstrating a requirement for a level of skill or application of knowledge)." Shouldn't be a problem.

So, if laws are interpreted the same way in Singapore, this may be an opportunity for enterprising fellows to set up an effectively zero-risk (pseudo-gambling?) operation. Is there a market for this? Likely yes, looking at the popularity of 4D and related games. Is it moral? Well, as moral as gambling in general is - personally I suppose the "skill" involved is not much better than, say, allowing people to roll a ten-sided dice for one of their numbers in 4D - though it must be said that coin tosses can be controlled to an astounding degree with enough practice.

A last caveat with these kinds of auctions is that it is certainly technically possible for the auctioneers to have a proxy insert a winning bid, with knowledge of the bids placed. Cries out for oversight, doesn't it?

Hammie Warz

Mr. Ham and Mr. Fish have resumed hostilities recently. The battle to be the dominant fuzzball appears to be a monthly occurrence. There have been suspicions that this is due to Mr. Ham attempting to innocently mount Mr. Fish when the mood takes him, but this has been vigorously denied by both hamsters.

Strangely, despite Mr. Fish probably being the better fighter when they get sorta serious (after protracted staring contests, Mr. Ham is always the one to run, squeaking away), Mr. Ham has a rather aggressive greeting ritual in peacetime - springing at Mr. Fish and licking the forehead, then optionally other body parts. Either case, Mr. Ham always gets United Nations support by acting as the victim, so all's right in their little world.

Left: Is the one on top the blanket, or is the one at the bottom the mattress?
Right: I demand U.N. protection!!!


While going through the site links, I discovered that not all that many 4O-related blogs are still up - what a pity. Just for fun, I ran those that were into Wordle, "...a toy for generating 'word clouds' from text that you provide... giv(ing) greater prominence to words that appear more frequently in the source text".

I would have given out an AAAAA to the first one to correctly identify all seven blogs from their word clouds, but then realised it wasn't that hard actually.


You just can't make stuff like this up. I thought I had seen it all when Samuel Eto'o considered a move from Barcelona to a Uzbekistani club, Kuruvchi (sorry, can't get Borat's Kazakh National Anthem out of my head). Then, a linesman awarded a "ghost goal" (video) for Reading despite the ball being nowhere near the line.

Then, news came out that Nigerian businessmen were out to buy Newcastle United.

Of course, Newcastle (together with Spurs) were already providing all-around comic relief this season (bolstered by new Newcastle manager Joe Kinnear peppering his first interview with a few dozen choice expletives), but Nigerian businessmen! I think I've gotten enough emails from them to be justified in guessing at the form of their offer:




I'll just stick to pretending to punt, thanks ($478.25/$600 now):

$50 on Arsenal (-1.5) vs. Sunderland (at 2.15)

Oh, and if ever I have to pretend to drink, I'll take Carlton Draught (N.B. its set to O Fortuna).

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