Advancing Fair Division Under Constraints

The field of fair division research is witnessing significant advancements, particularly in the context of constrained settings. Researchers are increasingly focusing on achieving both fairness and efficiency in the allocation of indivisible goods under various constraints, such as matroid constraints and non-matroidal constraints. The concept of maximum Nash welfare (MNW) is proving to be remarkably effective in these scenarios, offering strong guarantees of envy-freeness and Pareto optimality. Additionally, there is a growing interest in developing polynomial-time algorithms for fair and efficient allocations, especially when the number of agents is fixed. These developments not only address theoretical challenges but also pave the way for practical implementations in real-world scenarios. Furthermore, improvements in maximin share approximations for chores are being explored, with new algorithms providing better approximations and identifying specific cases where exact MMS allocations are possible.

Sources

Constrained Fair and Efficient Allocations

The Fairness of Maximum Nash Social Welfare Under Matroid Constraints and Beyond

A Polynomial-Time Algorithm for Fair and Efficient Allocation with a Fixed Number of Agents

Improved Maximin Share Approximations for Chores by Bin Packing

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