Description
Several players wish to share, over the long run, which of them gets to
receive a certain indivisible good on each day. For example, one player
values the good equally on every day. Another values it 1 on a random
one third of the days and values 0 on the others. A third player’s
valuation is drawn independently each day from the uniform distribution
on [0,1]. What allocation rule should we use to make the outcome both
efficient and fair?
Although fairness is ultimately a subjective notion, we show that in
this setting it can be defined in a robust way up to a factor of 1.283.
As a consequence of this theorem, we also obtain a 1.283-approximation
mechanism even when players may strategically misreport their
preferences.
The proof of the main theorem is about 20 pages long and was developed
jointly with ChatGPT. My talk will focus primarily on how artificial
intelligence can be used effectively for problems of this kind.
Zoom: https://zoom.us/j/2961946869?omn=98245035028