What if enrolling in classes at Cornell University became an auction?
In my Networks class at Cornell University, Professor Easley and Professor Halpern have discussed many interesting topics involving game theory. In particular, auctions have been one of the most fascinating topics we have learned about. Recently, the class roster for Spring 2022 has been released for Cornell students to plan out their schedule for pre-enrollment. The class roster is a database of all available courses at Cornell University and their time slots for a specified semester. In my case, the class roster website was for Spring 2022. The website includes many features such as filtering based on the department, college, time offered, day of the week, number of credits, etc. As I was planning my schedule for next semester, I recalled my experience during the freshmen pre-enrollment period, wondering what would happen if Cornell hosted an auction for enrollment. Of course, this process would be extremely complicated due to the high number of students at Cornell. Because of this, let’s assume that the auction is only hosted if there is one single spot left for that class.
My Networks course discussed four different types of auctions:
- Ascending Bid (English) – “price increases until only one bidder left”
- Descending Bid (Dutch) – “price decreases until someone accepts”
- First Price Sealed Bid – “highest bidder wins and pays their bid”
- Second Price Sealed Bid – “highest bidder wins and pays the second highest bid”
Before we dive deeper into each of these types of auctions, there are some keywords and ideas that we need to identify. In our scenario, Cornell University is the seller and the students are the bidders. Each bidder i has a value v sub i and bid b sub i. Referring back to the class roster website, the filters on the right side of the screen mentioned earlier can be used for students to create their value for that class. For example, a student may have a higher value for a 3000 level course than a 1000 level course. Additionally, the time offered can also be another factor that can affect a student’s value for that course. We can assume that seniors will have a higher value than juniors, juniors will have a higher value than sophomores, and sophomores will have a higher value than freshmen. If the course is required, then the student will have a higher value than if the student had alternatives. For example, if two senior students plan to enroll in the same course, then the student that chooses the course because it is an “easy” course and is not required will have a lower value than the other student who is absolutely required to take the course. All of these factors can affect a student’s value for the course.
Instead of having separate auctions for each grade level, we will have an auction for every course offered for that semester for all Cornell students that are interested in the course. For simplicity, the item being sold is the last slot available for the class. We should also assume that there is no cheating in these auctions, but any student is allowed to lie (in other words, they do not have to bid their value). Of course, there are lots of flaws to this. If a student really wants a class, then they can easily lie and bid above their true value. To counter this, let’s assume that every bid and value corresponds to an amount of money, that way there is a reasonable negative payoff to bidding above their value.
Let’s begin with the Ascending Bid auction (English auction), which in my opinion, will be the most chaotic and will likely crash the server due to having to constantly update. Each student has their own value for the course and is able to bid any amount they wish. There is a starting price for the course. To place a bid, the student simply inputs their amount and clicks on the “Bid” button on the screen. On everyone’s screen, there will be a live update of the current highest bid along with a timer that will indicate that the auction is over once the time runs out. What is the dominant strategy for this type of auction? Every student should stay in until their value is reached. In other words, the student should never bid above their value. The winner will receive the last spot. I do not recommend using this auction due to the high likelihood of crashing the server.
For the Descending Bid auction (Dutch auction), it will probably be less chaotic. There is a very high starting price for the course. On each student’s screen, the current price is displayed and the price gradually decreases. Instead of inputting a bid amount, there is only one button that the student can click. Once a student clicks the “Accept” button, the auction is over. There is no dominant strategy in this auction; however, the student should never accept when the current price is above or equal to their value because this results in a negative payoff. The winner gets the last spot and pays the price equal to the current price. This auction is not as bad as the English auction; however, it is still inefficient on the student’s side. If two students click accept at the same time, the server sees the student with the faster connection first.
For the First-Price Sealed Bid auction, it will be much more efficient than both the English and Dutch auctions. On each student’s screen, there is a box where a student can input their bid (similar to that of the English auction). There is also a timer indicating when the server will stop accepting responses. Once the timer is over, the server picks the student with the highest bid. The winner is the student with the highest bid, and they pay the price of their bid for the last spot. Because of this, there is no dominant strategy; however, the student should only bid less than their value. As we can see, sealed bids are very efficient in the way that the student’s network connection does not play an important role like it did in the Dutch auction. Also, it is less likely to crash the server because the only update going on is the timer.
Similarly, the Second-Price Sealed Bid auction offers the same exact benefits as the First-Price. The only difference is the strategy for the bidder and the amount the winner pays. The process is exactly the same as the first price sealed bid auction. This time, there is a dominant strategy. Since the winner wins the last spot and pays the second highest bid, every student should always bid truthfully (in other words, bid their own value) despite knowing the bidding strategy of other students.
Both the first-price and second-price sealed bid auctions are great methods that Cornell could implement. Even though it is highly unlikely that there will be an auction for the last spot of a class, it is really interesting to see how we can connect game theory and auctions to almost any kind of event.
Sources:
https://classes.cornell.edu/browse/roster/SP22
https://classes.cornell.edu/content/FA21/faq
https://registrar.cornell.edu/classes-enrollment/student-center-faq