Course bidding: Is auction always the best?

I’m back to Harvard where I have to decide on which classes to take in the new semester. Naturally, some classes (or professors) are more popular – much more popular – than others. So there exists a natural economic question: how should we allocate the scarce resources (seats) to all the students?

The Harvard Kennedy School and Harvard Business School have offered very different solutions to the same problem. At the HKS, students are allocated “points” so that they can “bid” for a class if the number of students wanting to enroll exists the number of seats. Each student has up to 1000 points to use in the whole year. And if the clearing “price” is less than you bid, you will get the extra points back.

That sounds like a fair system and a simple economic model, where supply and demand determines a equilibrium price and quantity (which is capped). But closer examination of the system raises some questions. In this year, the most expensive class goes to Ronald Heifetz’s “Leadership” – at 998 points! The high price has no problem in itself, after all, if you are willing to (almost) give up bidding any other classes just to do “Leadership”, it is entirely your choice. But what will happen next year? Students who observed this price would either bid 1000 points, so they can take the course for sure, or zero point, because you will think that placing 900 points in the bid would not get you into the class, so why even bid for it? This would discourage some people to even enter into the “marketplace”. And if there are sufficient amount of people who would decide not to bid, in some year you may be able to win the class by just bidding for one point! That is to say, the clearing price of the most popular course would likely fluctuate a lot between zero and 1000.

Just across the river, the HBS has a different system. There are 900 MBA students a year, and around 60 elective courses. Every student would have to put the preference of the 60 courses from one to 60. Then, students would be randomly assigned a number from one to 900, with student “one” being allocated her top choice. Student “two” would then get her top choice, and so on. If the top choice for student “900” is already full when it gets to her round, she will then get her second choice (if that is full too, her third choice). After the first round, each student would have got one course. Then the same process goes into the second round – this time starting from student “900”. The same process goes on until all the courses are allocated. Therefore, each student should get a combination of “good” and “bad” courses in this system.

This example shows that price theory may have its limit, and indeed, price may not always be the best tool for an economy to allocate resources. The HBS model owes very much to the pioneering ideas of Alvin Roth, then a Harvard professor, and last year’s Nobel laureate in economics. His researches in “market design” and “top trading cycle” have helped patients to get kidneys, universities to admit students, men and women to find their spouses – “markets” where price does not actually work that well. For interested readers, you can visit Professor Roth’s blog here.

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