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

The theory of algorithmic fair allocation is at the center of multi-agent systems and economics in recent decades 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. In this survey, we focus on indivisible items, for which exact fairness as measured by envy-freeness and proportionality cannot be guaranteed. One main theme in the recent research agenda is designing algorithms that approximately achieve fairness criteria. We aim at presenting a comprehensive survey of recent progressthrough 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.