Approximation Algorithms for Maximin Fair Division

Approximation Algorithms and Hardness Results for Fair Division with Indivisible Goods

An Empirical Evaluation of Fair-Division Algorithms

Fair-division problems are ubiquitous. They range from the day-to-day chore assignments to the Israeli-Palestinian conflict and include the division of an inheritance to the heirs (Brams & Taylor, 1999; Massoud, 2000). Many intuitive and self-implementable algorithms guaranteeing “fairness” have been devised in the past 50 years (Brams & Taylor, 1996). So far, very few empirical studies have pu...

X Fair Enough: Guaranteeing Approximate Maximin Shares

We consider the problem of fairly allocating indivisible goods, focusing on a recently-introduced notion of fairness called maximin share guarantee: Each player’s value for his allocation should be at least as high as what he can guarantee by dividing the items into as many bundles as there are players and receiving his least desirable bundle. Assuming additive valuation functions, we show that...

Groupwise Maximin Fair Allocation of Indivisible Goods

We study the problem of allocating indivisible goods among n agents in a fair manner. For this problem, maximin share (MMS) is a well-studied solution concept which provides a fairness threshold. Specifically, maximin share is defined as the minimum utility that an agent can guarantee for herself when asked to partition the set of goods into n bundles such that the remaining (n− 1) agents pick ...

Fair Division*

Properties of discrete cake-cutting procedures that use a minimal number of cuts (n – 1 if there are n players) are analyzed. None is always envy-free or efficient, but divideand-conquer (D&C) minimizes the maximum number of players that any single player may envy. It works by asking n ≥ 2 players successively to place marks on a cake that divide it into equal or approximately equal halves, the...