Fair and Efficient Online Allocations with Normalized Valuations

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 fair while guaranteeing 91.6% of the optimal social welfare. We also show that this is near-optimal: there is no fair algorithm that guarantees more than 93.3% of the optimal social welfare.