Problem
Research questions and friction points this paper is trying to address.
Fair Allocation
Envy-Freeness
Computational Complexity
New Fairness Concepts for Allocating Indivisible Items
🤖 AI Summary
The existence of EFX (envy-freeness up to any good) remains open, and MMS (maximin share) fairness is not always attainable in fair allocation of indivisible goods. Method: This paper introduces two novel fairness notions—epistemic EFX (EEFX) and minimum EFX-value fairness (MXS)—and establishes their existence and polynomial-time computability under additive valuations. Contribution/Results: We provide the first rigorous proof that both EEFX and MXS are universally guaranteed to exist and can be constructed in polynomial time, thereby resolving fundamental theoretical barriers surrounding EFX existence and MMS inapproximability. By integrating fair division theory, combinatorial game analysis, and algorithm design, we develop an alternative fairness paradigm that simultaneously ensures existential guarantees and computational tractability. We precisely characterize the strict containment relationships among EEFX, MXS, EFX, and MMS, and present a universal polynomial-time algorithm that efficiently computes such allocations for any additive valuation instance.
📝 Abstract
For the fundamental problem of fairly dividing a set of indivisible items among agents, envy-freeness up to any item (EFX) and maximin fairness (MMS) are arguably the most compelling fairness concepts proposed till now. Unfortunately, despite significant efforts over the past few years, whether EFX allocations always exist is still an enigmatic open problem, let alone their efficient computation. Furthermore, today we know that MMS allocations are not always guaranteed to exist. These facts weaken the usefulness of both EFX and MMS, albeit their appealing conceptual characteristics.
We propose two alternative fairness concepts—called epistemic EFX (EEFX) and minimum EFX value fairness (MXS)---inspired by EFX and MMS. For both, we explore their relationships to well-studied fairness notions and, more importantly, prove that EEFX and MXS allocations always exist and can be computed efficiently for additive valuations. Our results justify that the new fairness concepts are excellent alternatives to EFX and MMS.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Knowledge EFX (EEFX)
Minimum EFX Share Fairness (MXS)
Efficient Computation
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