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We study fair allocation of indivisible goods among agents with additive valuations. Our main result guarantees every agent her exact AnyPrice Share (APS) whenever the total entitlement is at most $1-\varepsilon$ and each individual entitlement is sufficiently small. For equal entitlements, this yields a $1$-out-of-$(n...
The maximin share (MMS) is a central fairness benchmark for allocating indivisible items, but it need not be simultaneously attainable even under additive preferences. While extensive work has developed approximation guarantees, quantitative impossibility bounds have received comparatively little attention. We establis...
We settle the worst-case approximability of consumer-surplus maximization in general multidimensional mechanism-design environments. We do so through two black-box reductions from welfare maximization to the agents'total utility. Our first reduction turns exact welfare maximization into a prior-free, universally truthf...
We settle the worst-case approximability of residual-surplus maximization in general multidimensional mechanism-design environments. For $n$ agents with arbitrary nonnegative valuations over a finite outcome space, we give a universally truthful and ex-post individually rational mechanism whose expected residual surplu...
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