Algorithmic Fair Allocation of Indivisible Items: A Survey and New Questions

The theory of algorithmic fair allocation is within the center of multi-agent systems and economics in the last decade due to its industrial and social importance. At a high level, the problem is to assign a set of items that are either goods or chores to a set of agents so that every agent is happy with what she obtains. Particularly, in this survey, we focus on indivisible items, for which absolute fairness such as envy-freeness and proportionality cannot be guaranteed. One main theme in the recent research agenda is about designing algorithms that approximately achieve the fairness criteria. We aim at presenting a comprehensive survey of recent progresses through the prism of algorithms, highlighting the ways to relax fairness notions and common techniques to design algorithms, as well as the most interesting questions for future research.