Nash Social Welfare for Indivisible Items under Separable, Piecewise-Linear Concave Utilities
Computer Science and Game Theory
2017-04-10 v3 Discrete Mathematics
Data Structures and Algorithms
Combinatorics
Abstract
Recently Cole and Gkatzelis gave the first constant factor approximation algorithm for the problem of allocating indivisible items to agents, under additive valuations, so as to maximize the Nash Social Welfare. We give constant factor algorithms for a substantial generalization of their problem -- to the case of separable, piecewise-linear concave utility functions. We give two such algorithms, the first using market equilibria and the second using the theory of stable polynomials. In AGT, there is a paucity of methods for the design of mechanisms for the allocation of indivisible goods and the result of Cole and Gkatzelis seemed to be taking a major step towards filling this gap. Our result can be seen as another step in this direction.
Keywords
Cite
@article{arxiv.1612.05191,
title = {Nash Social Welfare for Indivisible Items under Separable, Piecewise-Linear Concave Utilities},
author = {Nima Anari and Tung Mai and Shayan Oveis Gharan and Vijay V. Vazirani},
journal= {arXiv preprint arXiv:1612.05191},
year = {2017}
}