Uniform Welfare Guarantees Under Identical Subadditive Valuations

We study the problem of allocating indivisible goods among agents that have an identical subadditive valuation over the goods. The extent of fair- ness and efficiency of allocations is measured by the generalized means of the values that the alloca- tions generate among the agents. Parameterized by an exponent term p, generalized-mean welfares en- compass multiple well-studied objectives, such as social welfare, Nash social welfare, and egalitarian welfare. We establish that, under identical subadditive valu- ations and in the demand oracle model, one can efficiently find a single allocation that approximates the optimal generalized-mean welfare—to within a factor of 40—uniformly for all p ∈ (−∞,1]. Hence, by way of a constant-factor approximation algorithm, we obtain novel results for maximizing Nash social welfare and egalitarian welfare for identical subadditive valuations.