Fair Allocation of goods and chores -- Tutorial and Survey of Recent Results

TL;DR

This survey reviews recent advances in fair allocation of indivisible goods and chores, discussing algorithms, fairness criteria, computational complexity, and trade-offs to guide future research in resource distribution.

Contribution

It provides a comprehensive overview of the latest results, algorithms, and complexity analyses in fair allocation of indivisible resources, highlighting open challenges and future directions.

Findings

Survey of algorithms satisfying various fairness criteria

Analysis of computational complexity and fairness trade-offs

Discussion of mixed divisible and indivisible resource instances

Abstract

Fair resource allocation is an important problem in many real-world scenarios, where resources such as goods and chores must be allocated among agents. In this survey, we delve into the intricacies of fair allocation, focusing specifically on the challenges associated with indivisible resources. We define fairness and efficiency within this context and thoroughly survey existential results, algorithms, and approximations that satisfy various fairness criteria, including envyfreeness, proportionality, MMS, and their relaxations. Additionally, we discuss algorithms that achieve fairness and efficiency, such as Pareto Optimality and Utilitarian Welfare. We also study the computational complexity of these algorithms, the likelihood of finding fair allocations, and the price of fairness for each fairness notion. We also cover mixed instances of indivisible and divisible items and investigate different valuation and allocation settings. By summarizing the state-of-the-art research, this survey provides valuable insights into fair resource allocation of indivisible goods and chores, highlighting computational complexities, fairness guarantees, and trade-offs between fairness and efficiency. It serves as a foundation for future advancements in this vital field.