Online Fair Allocations with Binary Valuations and Beyond

TL;DR

This paper investigates online fair allocation of indivisible items, focusing on fairness and efficiency for binary and bi-valued valuations, providing positive results and optimality bounds.

Contribution

It introduces new algorithms and bounds for online fair allocations with binary and bi-valued valuations, extending fairness notions like EF1 and MMS.

Findings

Existence of fair and efficient online allocations under binary valuations

Counterexamples showing the tightness of the results

Positive algorithms for both goods and chores allocation

Abstract

In an online fair allocation problem, a sequence of indivisible items arrives online and needs to be allocated to offline agents immediately and irrevocably. In our paper, we study the online allocation of either goods or chores. We employ popular fairness notions, including envy-freeness up to one item (EF1) and maximin share fairness (MMS) to capture fairness, and utilitarian social welfare (USW) to measure efficiency. For both settings of items, we present a series of positive results regarding the existence of fair and efficient allocations with widely studied classes of additive binary and personalized bi-valued valuation/cost functions. Furthermore, we complement our results by constructing counterexamples to establish our results as among the best guarantees possible.