Wednesday, January 07, 2009

CORS : Iterated Prisoner's Dilemma

As I placed and won my CORS module bid, using an insane showhand bid of 6000+ points, for probably the last time in my undergraduate times, it suddenly dawned upon me that CORS bidding was a game of iterated prisoner's dilemma.

There are many 'strategies' for CORS bidding, but probably the strategy with the most effect is to deny all opponents of additional information, i.e., to not submit any bids during the open bidding phase. Conversely, by submitting an accurate bid (a bid that is valued according to your evaluation of the worth of the module), your bid provides information to potential competitors.

Of course, if everyone is selfish and does not contribute accurate bids, then the open phase is defeated, and everyone's utility is hampered.

Expressing the above in a game table,
Now, since the results of bidding are only known after the bidding has concluded, and that students have other semesters left, this provides some kind of force against concealing your bid. The rationale is that if everyone finds out that they have been exploited due to revealing their bids, then they too could retaliate by not revealing their bids the next time round. Hence, everyone loses, and overall utility is reduced. Everyone realizes that their utility is best optimized by maintaining the status quo.

The situation, however, is disturbed by people who have no fear of retaliation, i.e. final year students. Hence, they tend to do funny things to the system, i.e. random bids, showhand bids, or just hogging multiple candidate modules before dropping them.

Problem is, if the system is indeed an iterated prisoner's dilemma, then knowing that final year students would do X in their final year, one intuitively realizes that during their 3rd year, the force of the contract is nonexistent, since "good" behavior in year 3 does not influence others to behave well in their final years. Extend this argument, and one realizes that the system is unstable.

Sunday, January 04, 2009

The Sand Reader

There was once a small town set in the countryside. Though life in those times was simple, this did not mean everything ran smoothly and without a problem. There were of course the kinds of hiccups that happened once every while, or even the rare and extraordinary disasters that could affect many in the town. The town was fortunate, though, for within the town resided an enigmatic person who read the sands.

Any person who was plagued by problems of any nature, whether minor or major, could approach the sand reader to have his problem addressed. The sand reader would first listen to the person's problem, and then pour out some sand from a special flask into a large pan. Then, the sand reader would manipulate the sand within the pan with his hands, and interpret the resulting patterns formed. By 'reading' the sand, any problem could be resolved.

The advice of the sand reader was always accurate and true. The townsfolk were in awe of the sand reader's ability, and some even wanted to know how to read the sands. The more foolish would head to the beaches and attempt to interpret the sand there. The more daring would sneak into the sand reader's home while he was asleep or out and attempt to read his sand. Neither approach would result in anything concrete.

There was one young man who was interested in learning the skill of sand reading. For each day of the year he would consult the sand reader with a problem, whether real or imagined, and closely observe how the sand reader moved and read the sands. Immediately after the consultation, he would run home and record his observations into his book. Once in a while he would repeat a question that he had asked during his previous visits, or a question that another person had asked previously. Everything was recorded in his book.

After about a year of visits, the young man realized something odd. Sometimes, the sand patterns were similar, but the readings were absolutely different. On other occasions, the readings were alike, yet the sand patterns were totally dissimilar. Puzzled, the young man approached the sand reader for an explanation. The sand reader surmised that the young man wanted to learn the skill of sand reading, and the young man verified this. After some thinking, the sand reader decided to reveal one of the secrets to his skill, and instructed the young man to collect one grain of sand from a beach daily. Furthermore, only sand collected in such a way could be used to perform readings.

Excited by the revealed secret, each day, the man collected one grain of sand from a nearby beach, while continuing his usual consultation with the sand reader. After three years, the young man had collected a sizable amount of sand, but it was nowhere near the amount needed to read sand in a pan. The young man decided to approach the sand reader for advice.

"I have only collected this amount of sand after three years. How long do you think I need to amass sufficient sand to do a reading? Is there a better or faster method?"

The sand reader merely asked the young man to produce his own estimate.

"I judge, based on the relative amounts of sand, that I would need at least 10 more years to collect enough sand to do a reading."

The sand reader smiled, and told the young man to carefully scrutinize the sands, and to arrive at a better estimate.

Puzzled, the young man stared at the sand reader's sand, and at his own sand. After a while, he realized that while each grain of his own sand was roughly of the same coarseness and color, the sand reader's sand was of many different sizes and colors. The young man spent some more time in careful study, before breaking out in a laugh.

"I understand now! My initial estimate was wrong - if I were to collect sand daily from the nearby beach, I would never be able to collect enough sand to perform a reading!"

The sand reader nodded, and asked if the young man still wanted to walk the path of sand reading.

The young man said yes, and received the blessing of the sand reader. The very next day, the young man left the town on a long and great journey, a trip to collect the sands of knowledge and experience that can only be found in the world beyond the beaches of the town.