Dear class (those of you taking the course for credit), we're
approaching the final lecture slots, in which you will do your
presentations. Given the number of people in the course, we'll need
three lecture slots for the presentations. With graduate course
lectures ending on 4/20, that means we'll have to start project
presentations next week on Wednesday, so we don't have much time. I
imagine that all else being equal, most of you would prefer the later
slots. How do we resolve this? With incentives, of course -- we're
going to run an auction that gives teams a points incentive to take an
earlier slot! Below is a description of how this will work. I will
take questions on this auction design in class on Wednesday, and make
bids on slots due this Thursday 11:59pm, by e-mail to me, so that if
all goes well we can discuss the outcome in class on Friday.
*If you fail to bid, I will simply interpret your bid as all 0s.*
Hopefully this will be fun. There will be presentation slots on 4/13,
4/15, and 4/20. Please note that the final project *writeup* will be
due later, so it's not required that you already have all your results
for the presentation; it's fine to spend most of the time introducing
and discussing the problem in the presentation, though of course it
will be nice to have some results.
Here's how it's going to work. You are going to bid some number of
points for each presentation day before the last day (4/20, which is
presumably the most desirable). This bid represents the minimum
number of bonus points by which you want to be compensated for going
in a slot on that day. (This number is implicitly 0 for the slots on
the last day, and are relative to a possible score of 100 on the
presentation part of the project.) Then, to encourage truthful
bidding, we'll run the VCG mechanism. Here is an example (the example
has fewer slots than we'll need):
Suppose we have four slots, one on day 1, two on day 2, and one on day 3.
A bids 25, 10 (meaning, he wants to be compensated 25 for going on the
first day, and 10 for going on the second day (and implicitly 0 for
going on the last day))
B bids 30, 20
C (who is way behind on his project) bids 80, 30
D (who is in good shape on her project) bids 15, 10
First, we choose the solution that minimizes cost. This is to put D
on day 1, A and B on day 2, and C on day 3, for a total cost of
15+10+20=45.
Let's determine A's compensation. To do so, we will solve for the
optimal solution in which A goes last. This is D on day 1, and B and
C on day 2, for a total cost of 15+20+30=65. From this we subtract
15+20=35 (the cost to other students, D and B, in the real solution)
to obtain a compensation of 30 bonus points.
For B: the optimal solution with B last is: D on day 1 and A and C on
day 2 for a cost of 15+10+30=55. Subtract from this 15+10=25 to get a
compensation of 30 bonus points.
For C: C is already on the last day so the difference must be 0, i.e.,
C gets no bonus points.
For D: the optimal solution with D last is B on day 1 and A and C on
day 2 for a cost of 30+10+30=70. Subtract from this 10+20=30 to get a
compensation of 40 bonus points.
(You can see the incentive for having your project in good shape soon...)
Let me know if anything doesn't make sense (or if I made a mistake in
this example).
So, your bid should have two nonnegative numbers (probably decreasing)
separated by commas, e.g.
50, 30
represents you want to be compensated at least 50 points for going on
4/13 and at least 30 for going on 4/15 (and implicitly 0 for 4/20, the
last day). There should be one bid per project team. Bids larger
than 100 will not be allowed.
Please, no bids involving pi, e, or other craziness. No collusion, either
:-)
A note on presentations: please attend your classmates' presentations
(part of the participation part of the grade, but also just out of
respect for your classmates), and in turn, when you give your
presentation, keep your classmates in mind, i.e., they should be able
to follow what you're doing. Focus on the parts most related to the
course, and make sure to introduce the problem well so that everyone
understands.
Please let me know if you have any questions or concerns. Also please
remember I am here to help. I look forward to your project
presentations!