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On Fair and Efficient Allocations of Indivisible Public Goods

Authors Jugal Garg, Pooja Kulkarni, Aniket Murhekar

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Author Details

Jugal Garg
  • University of Illinois, Urbana-Champaign, IL, USA
Pooja Kulkarni
  • University of Illinois, Urbana-Champaign, IL, USA
Aniket Murhekar
  • University of Illinois, Urbana-Champaign, IL, USA

Funding

Supported by NSF Grant CCF-1942321 (CAREER).

Cite AsGet BibTex

Jugal Garg, Pooja Kulkarni, and Aniket Murhekar. On Fair and Efficient Allocations of Indivisible Public Goods. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 22:1-22:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.FSTTCS.2021.22

Abstract

We study fair allocation of indivisible public goods subject to cardinality (budget) constraints. In this model, we have n agents and m available public goods, and we want to select k ≤ m goods in a fair and efficient manner. We first establish fundamental connections between the models of private goods, public goods, and public decision making by presenting polynomial-time reductions for the popular solution concepts of maximum Nash welfare (MNW) and leximin. These mechanisms are known to provide remarkable fairness and efficiency guarantees in private goods and public decision making settings. We show that they retain these desirable properties even in the public goods case. We prove that MNW allocations provide fairness guarantees of Proportionality up to one good (Prop1), 1/n approximation to Round Robin Share (RRS), and the efficiency guarantee of Pareto Optimality (PO). Further, we show that the problems of finding MNW or leximin-optimal allocations are NP-hard, even in the case of constantly many agents, or binary valuations. This is in sharp contrast to the private goods setting that admits polynomial-time algorithms under binary valuations. We also design pseudo-polynomial time algorithms for computing an exact MNW or leximin-optimal allocation for the cases of (i) constantly many agents, and (ii) constantly many goods with additive valuations. We also present an O(n)-factor approximation algorithm for MNW which also satisfies RRS, Prop1, and 1/2-Prop.

Subject Classification

ACM Subject Classification
  • Theory of computation → Mathematical optimization
Keywords
  • Public goods
  • Nash welfare
  • Leximin
  • Proportionality

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