Game

At a meeting last week, CM explained the rules of choosing postgraduate students in the department. I beamed at my mentor. “Game theory!”

It goes like this. First, each department chooses a number of postgraduate students according to the assigned quota. These students would certainly be recruited. After that, there will still be vacancies in the whole faculty. Each department would then select candidates from the remaining list for central bidding. The latter students would compete with candidates recommended by other departments. Those with the best academic results would get the remaining seats.

Let’s ignore the issue of fairness for the time being. The central bidding step is the most fascinating part of the whole process. If we place less impressive candidates in the guaranteed list and pose the best students for central bidding, we would have a higher chance of getting more students for the department but also risk losing the best candidates. Conversely, if we put the best candidates in the guaranteed list and recommend the rest for central bidding, we for sure will retain the candidates we want but would less likely get extra students.

In game theory jargons, since the total number of vacancies for central bidding is fixed each year, this is a multi-person, zero-sum game. The payoff is the number of extra students obtained. Assuming that the quality of applicants in each department is similar, we can presume that a department will have almost 100% chance of winning if it sends the best candidate for bidding while other departments send those on the waiting list. Similarly, a department will have nearly zero chance of winning if it sends a waiting list candidate for bidding while others send the best ones. When two departments send the best or the so-so candidates for bidding at the same time, we can assume that the chance of either winning would be 50-50. The probability will decrease by proportion as more departments decide to send the best candidates.

In this situation, because there are multiple players in the game, the probability of having none of them choose the best (or very good) candidates for bidding is too trivial to consider seriously. Therefore, the only chance to win is to send the best student for the competition.

Then there is no need to hesitate, right? Not quite. In the above argument, the only payoff considered was the total number of extra candidates a department obtains. In reality, the perceived value of getting an extra candidate and that of losing a superb candidate should be taken into consideration too. That weighting is subjective.

I cannot say for others, but what is the perceived value for me?

That would be better explained by Cheshire Cat.

Alice: I was just wondering if you could help me find my way.

Cheshire Cat: Well that depends on where you want to get to.

Alice: Oh, it really doesn’t matter, as long as …

Cheshire Cat: Then it really doesn’t matter which way you go.