Uniform Welfare Guarantees Under Identical Subadditive Valuations
Abstract
We study the problem of allocating indivisible goods among agents that have an identical subadditive valuation over the goods. The extent of fairness and efficiency of allocations is measured by the generalized means of the values that the allocations generate among the agents. Parameterized by an exponent term $p$, generalizedmean welfares encompass multiple wellstudied objectives, such as social welfare, Nash social welfare, and egalitarian welfare. We establish that, under identical subadditive valuations and in the demand oracle model, one can efficiently find a single allocation that approximates the optimal generalizedmean welfareto within a factor of $40$uniformly for all $p \in (\infty, 1]$. Hence, by way of a constantfactor approximation algorithm, we obtain novel results for maximizing Nash social welfare and egalitarian welfare for identical subadditive valuations.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 DOI:
 10.48550/arXiv.2005.00504
 arXiv:
 arXiv:2005.00504
 Bibcode:
 2020arXiv200500504B
 Keywords:

 Computer Science  Computer Science and Game Theory
 EPrint:
 24 pages