Dear class,
As promised, we're going to hold an auction for the project presentation
slots. The explanation is below. (If you're doing a project) you must bid
by tomorrow (F) 11:59pm EST, by e-mail to me. Hopefully this will be fun.
There will be 3 slots on 4/5, 3 on 4/10, 2 on 4/12, and 2 on 4/17 (the
later presentations will get more time because they should have a little
more to talk about).
Here's how it's going to work. You are going to bid some number of points
for each day before the last day. 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 score of 100 on the presentation part of the project.)
Then we'll basically run VCG. Example:
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 his 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). How I'm going to solve the larger real instance is something
I'll have to deal with.
So, your bid should have 3 nonnegative numbers (probably decreasing)
separated by commas, e.g.
50, 30, 20
represents you want to be compensated at least 50 for going on 4/5, 30 for
4/10, 20 for 4/12 (and you won't get any bonus points for going on 4/17).
Please, no bids involving pi, e, or other craziness.
Best,
Vince