From multi-allocations to allocations, with subadditive valuations

TL;DR

This paper introduces a method to convert multi-allocations into standard allocations for agents with subadditive valuations, ensuring minimal loss in value and advancing fair division guarantees.

Contribution

It demonstrates that multi-allocations can be transformed into allocations with bounded value loss, improving fairness guarantees for subadditive valuation settings.

Findings

Transformation from multi-allocations to allocations with factor d loss

Existence of approximate MMS allocations under certain conditions

Improved bounds on fair division with subadditive valuations

Abstract

We consider the problem of fair allocation of $m$ indivisible items to $n$ agents with monotone subadditive valuations. For integer $d \ge 2$, a $d$-multi-allocation is an allocation in which each item is allocated to at most $d$ different agents. We show that $d$-multi-allocations can be transformed into allocations, while not losing much more than a factor of $d$ in the value that each agent receives. One consequence of this result is that for allocation instances with equal entitlements and subadditive valuations, if $\rho$-MMS $d$-multi-allocations exist, then so do $\frac{\rho}{4d}$-MMS allocations. Combined with recent results of Seddighin and Seddighin [EC 2025], this implies the existence of $\Omega(\frac{1}{\log\log n})$-MMS allocations.