Problem
Research questions and friction points this paper is trying to address.
indivisible goods allocation
subadditive valuations
maximin share (MMS)
maximum expectation share (MES)
fairness
On best of both worlds allocations with subadditive valuations
🤖 AI Summary
This study addresses the challenge of simultaneously satisfying ex-ante Maximum Expected Share (MES) and ex-post Maximin Share (MMS) fairness when allocating indivisible items under subadditive valuations. The authors propose the first general MMS-to-MES conversion framework, which transforms any deterministic ρ-MMS algorithm into a randomized one by integrating combinatorial optimization with game-theoretic tools for bound derivation. They demonstrate that the converted algorithm achieves η-MES (where η ≥ min[ρ/(2+ρ), 1/4]) while preserving the ρ-MMS guarantee, thereby revealing an intrinsic connection between these two fairness notions. Furthermore, this work establishes the existence of simultaneous Ω(1/log log n)-MES and Ω(1/log log n)-MMS guarantees, and specifically derives 4/27-MES and 4/17-MMS bounds for XOS valuations.
📝 Abstract
We consider allocation of indivisible goods to agents with equal entitlements and subadditive valuations. As an ex-post fairness notion we consider the maximin share (MMS), and as an ex-ante fairness notion we consider the maximum expectation share (MES), which is always at least as large as the MMS, and sometimes much larger. We present a simple transformation that for every $0<\rho \le 1$, given any algorithm that produces $\rho$-MMS allocations, transforms it into a randomized allocation algorithm that offers $\rho$-MMS ex-post simultaneously with $\eta$-MES ex-ante. We prove several new properties of MES, and use them to show that $\eta \ge \min[\frac{\rho}{2 + \rho}, \frac{1}{4}]$. We also present cases in which the transformation results in a higher value of $\eta$. Applying our transformation to currently known allocation algorithms shows for subadditive valuations the existence of randomized allocations that are simultaneously $\Omega(\frac{1}{\log\log n})$-MES ex-ante and $\Omega(\frac{1}{\log\log n})$-MMS ex-post, and for XOS valuations the existence of randomized allocations that are simultaneously $\frac{4}{27}$-MES ex-ante and $\frac{4}{17}$-MMS ex-post.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Subadditive valuations
Maximin share (MMS)
Maximum expectation share (MES)
Randomized allocation
Fair division
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