Approximations for Indivisible Concave Allocations with Applications to Nash Welfare Maximization


  • Nathaniel Kell Denison University
  • Kevin Sun Elon University



GTEP: Fair Division, GTEP: Auctions and Market-Based Systems, GTEP: Other Foundations of Game Theory & Economic Paradigms, SO: Local Search, SO: Other Foundations of Search & Optimization


We study a general allocation setting where agent valuations are concave additive. In this model, a collection of items must be uniquely distributed among a set of agents, where each agent-item pair has a specified utility. The objective is to maximize the sum of agent valuations, each of which is an arbitrary non-decreasing concave function of the agent's total additive utility. This setting was studied by Devanur and Jain (STOC 2012) in the online setting for divisible items. In this paper, we obtain both multiplicative and additive approximations in the offline setting for indivisible items. Our approximations depend on novel parameters that measure the local multiplicative/additive curvatures of each agent valuation, which we show correspond directly to the integrality gap of the natural assignment convex program of the problem. Furthermore, we extend our additive guarantees to obtain constant multiplicative approximations for Asymmetric Nash Welfare Maximization when agents have smooth valuations. This algorithm also yields an interesting tatonnement-style interpretation, where agents adjust uniform prices and items are assigned according to maximum weighted bang-per-buck ratios.




How to Cite

Kell, N., & Sun, K. (2023). Approximations for Indivisible Concave Allocations with Applications to Nash Welfare Maximization. Proceedings of the AAAI Conference on Artificial Intelligence, 37(5), 5705-5713.



AAAI Technical Track on Game Theory and Economic Paradigms