Tight Lower Bounds for Unequal Division
Computer Science and Game Theory
2012-06-08 v1
Abstract
Alice and Bob want to cut a cake; however, in contrast to the usual problems of fair division, they want to cut it unfairly. More precisely, they want to cut it in ratio . (We can assume gcd(a,b)=1.) Let f(a,b) be the number of cuts will this take (assuming both act in their own self interest). It is known that f(a,b) \le \ceil{lg(a+b)}. We show that (1) for all a,b, f(a,b) \ge lg(lg(a+b)) + (2) for an infinite number of (a,b), f(a,b) \le 1+lg(lg(a+b).
Cite
@article{arxiv.1206.1553,
title = {Tight Lower Bounds for Unequal Division},
author = {Andrew Lohr},
journal= {arXiv preprint arXiv:1206.1553},
year = {2012}
}