Monotone and Online Fair Division

TL;DR

This paper introduces a new model for online fair division with indivisible items and monotone utilities, analyzing axiomatic properties and proposing mechanisms with good fairness guarantees under certain restrictions.

Contribution

It presents a novel online fair division model with monotone utilities, explores axiomatic limitations, and proposes mechanisms achieving fairness on restricted preference domains.

Findings

Impossibility results for strategy-proofness, envy-freeness, and Pareto efficiency.

Mechanisms with good fairness properties on restricted domains.

Justification for relaxing axiomatic properties and domain restrictions.

Abstract

We study a new but simple model for online fair division in which indivisible items arrive one-by-one and agents have monotone utilities over bundles of the items. We consider axiomatic properties of mechanisms for this model such as strategy-proofness, envy-freeness, and Pareto efficiency. We prove a number of impossibility results that justify why we consider relaxations of the properties, as well as why we consider restricted preference domains on which good axiomatic properties can be achieved. We propose two mechanisms that have good axiomatic fairness properties on restricted but common preference domains.