EF1-Constrained Nash Social Welfare with Identical Additive Valuations
ORIGINAL / EF1-Constrained Nash Social Welfare with Identical Additive Valuations: Complexity, Guarantees, and Experiments
This study systematically analyzes the relationship between EF1 allocations and Nash social welfare under identical additive valuations. Key findings show that any EF1 allocation is NSW-optimal under uniform valuations, and under an ε-small-item condition, EF1 allocations achieve an approximation ratio of 1-O(ε^2). The proposed PriorityNet deep reinforcement learning framework ensures prefix-wise EF1 with high performance.
01 ABSTRACT
The paper studies indivisible goods allocation under identical additive valuations, focusing on EF1 and NSW. Facts: maximum-NSW allocations are EF1, so threshold problem is strongly NP-complete; uniform valuations imply EF1 allocations are NSW-optimal; ε-small-item condition yields explicit approximation ratio; PriorityNet achieves mean normalized NSW of 0.9911 (offline) and 0.9701 (online). Authors argue PriorityNet guarantees prefix EF1 without post-processing and outperforms baselines.
02 KEY FINDINGS
- Maximum-NSW allocations are EF1 under identical additive valuations, making the threshold problem strongly NP-complete
- Under uniform valuations, every EF1 allocation is NSW-optimal
- Under ε-small-item condition, EF1 allocations achieve 1-O(ε^2) approximation
- PriorityNet deep reinforcement learning ensures prefix-wise EF1 via prospective masking
- PriorityNet achieves mean normalized NSW of 0.9911 (offline) and 0.9701 (online) in experiments
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