Strategy-proofness, Envy-freeness and Pareto efficiency in Online Fair Division with Additive Utilities

TL;DR

This paper explores online fair division with indivisible items and additive utilities, proposing new mechanisms and analyzing their strategy-proofness, envy-freeness, and Pareto efficiency, along with an important impossibility result.

Contribution

It introduces three new online mechanisms and characterizes classes of mechanisms with desirable fairness and efficiency properties in online settings.

Findings

Proposed three new online mechanisms for fair division.

Characterized classes of mechanisms that are strategy-proof, envy-free, and Pareto efficient.

Identified an important impossibility result in online fair division.

Abstract

We consider fair division problems where indivisible items arrive one-by-one in an online fashion and are allocated immediately to agents who have additive utilities over these items. Many existing offline mechanisms do not work in this online setting. In addition, many existing axiomatic results often do not transfer from the offline to the online setting. For this reason, we propose here three new online mechanisms, as well as consider the axiomatic properties of three previously proposed online mechanisms. In this paper, we use these mechanisms and characterize classes of online mechanisms that are strategy-proof, and return envy-free and Pareto efficient allocations, as well as combinations of these properties. Finally, we identify an important impossibility result.