Quote from ASusilovic:
Hi altogether,
I suppose some Quants visting ET...In a couple of days I will have the opportunity to question a quant working at Renaissance Technologies ( for the Renaissance Instutional Futures Fund ). As I am NOT A QUANT, I would like to ask ET members whether somebody has some brilliant questions so that at least I would not pass up the chance...
I prefer serious input !
The Pie-Splitting Problem
Imagine that N=3 friends gather to make an apple pie. They buy the ingredients, they follow the recipe, they bake it, and finally they have a yummy apple pie.
The pie looks delicious, and the three friends canât wait to eat it up. However, they now have a problem: how should they split the pie in a fair manner? There are various possibilities, among which:
* equal division: before they start making the pie they could agree that each would get 1/3 of the pie once the pie is ready. However, since the reward is certain, one (or more) of the friends could then opt to slack off and do very little. Why should he bother if heâs gonna get 1/3 of the pie, right?
* the leader splits the pie: the three friends could elect a leader who would split the pie in the end. However, there obviously would be a conflict of interests: the leader would be more interested in having a big slice of the pie than in deciding fairly how the pie should be split.
* the arbiter splits the pie: the three friends could invite a fair and impartial arbiter to supervise the pie-making operation. In the end, the arbiter would try to assess (as fairly as possible) each cookâs contribution, and then decide how the pie should be split. However, what if the supposedly âfairâ arbiter and one of the cooks collude?
* distributed unhierarchical evaluation: before they start making the pie, the three friends could agree on an algorithm. Once the pie were ready, each friend would evaluate each of his friendsâ contribution, as well as his own. They would then rely on their pie-splitting algorithm to compute the âfairestâ splitting.
1) Given a set of rules and assumptions, what would be the optimal strategy?
2) what (good) pie-splitting algorithms can you think of?
