Envy-free House Allocation under Uncertain Preferences

TL;DR

This paper investigates the problem of allocating items envy-freely when agents' preferences are uncertain, analyzing various models and their computational complexities to find the most likely envy-free allocations.

Contribution

It provides a comprehensive analysis of the computational complexity of envy-free house allocation under different preference uncertainty models, including algorithms and inapproximability results.

Findings

Distinct complexity results for each preference uncertainty model

Algorithms for checking possible or necessary envy-freeness

Complexity classifications for all models considered

Abstract

We study the envy-free house allocation problem when agents have uncertain preferences over items and consider several well-studied preference uncertainty models. The central problem that we focus on is computing an allocation that has the highest probability of being envy-free. We show that each model leads to a distinct set of algorithmic and complexity results, including detailed results on (in-)approximability. En route, we consider two related problems of checking whether there exists an allocation that is possibly or necessarily envy-free. We give a complete picture of the computational complexity of these two problems for all the uncertainty models we consider.