Fair and Efficient Online Allocations with Normalized Valuations

TL;DR

This paper introduces an online allocation algorithm for two agents with normalized valuations that guarantees envy-freeness and near-optimal social welfare, overcoming impossibility results in adversarial settings.

Contribution

It presents the first online envy-free allocation algorithm with provable welfare guarantees under normalized valuations for two agents.

Findings

Ensures envy-freeness in online resource allocation for two agents.

Guarantees at least 91.6% of the optimal social welfare.

Proves that no envy-free algorithm can exceed 93.3% welfare guarantee.

Abstract

A set of divisible resources becomes available over a sequence of rounds and needs to be allocated immediately and irrevocably. Our goal is to distribute these resources to maximize fairness and efficiency. Achieving any non-trivial guarantees in an adversarial setting is impossible. However, we show that normalizing the agent values, a very common assumption in fair division, allows us to escape this impossibility. Our main result is an online algorithm for the case of two agents that ensures the outcome is envy-free while guaranteeing 91.6% of the optimal social welfare. We also show that this is near-optimal: there is no envy-free algorithm that guarantees more than 93.3% of the optimal social welfare.