Temporal Fair Division
Benjamin Cookson, Soroush Ebadian, Nisarg Shah

TL;DR
This paper investigates fair division of goods over time among agents, establishing existence results for various fairness guarantees in general and special cases, and highlighting the complexity of achieving multiple fairness criteria simultaneously.
Contribution
It introduces new fairness guarantees for temporal division, proves their existence in general and special cases, and explores the limits of these guarantees.
Findings
Existence of allocations that are SD-EF1 per day and PROP1 overall.
Guarantees for two agents using envy balancing techniques.
Counterexamples showing limits of simultaneous fairness guarantees.
Abstract
We study temporal fair division, whereby a set of agents are allocated a (possibly different) set of goods on each day for a period of days. We study this setting, as well as a number of its special cases formed by the restrictions to two agents, same goods on each day, identical preferences, or combinations thereof, and chart out the landscape of achieving two types of fairness guarantees simultaneously: fairness on each day (per day) and fairness over time (up to each day, or the weaker version, overall). In the most general setting, we prove that there always exists an allocation that is stochastically-dominant envy-free up to one good (SD-EF1) per day and proportional up to one good (PROP1) overall, and when all the agents have identical preferences, we show that SD-EF1 per day and SD-EF1 overall can be guaranteed. For the case of two agents, we prove that SD-EF1 per day and EF1…
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Taxonomy
TopicsGame Theory and Voting Systems · Auction Theory and Applications · Game Theory and Applications
