Doubly Fair Dynamic Pricing

TL;DR

This paper introduces a novel online dynamic pricing algorithm that ensures both procedural and substantive fairness constraints simultaneously, achieving near-optimal regret and fairness guarantees in a two-group setting.

Contribution

It proposes the first algorithm that learns dynamic prices satisfying two fairness constraints at once, with proven optimal regret and unfairness bounds.

Findings

Achieves $ ilde{O}( oot{T} otag)$ regret in two-group pricing.

Ensures zero procedural fairness violation.

Guarantees $ ilde{O}( oot{T} otag)$ substantive unfairness.

Abstract

We study the problem of online dynamic pricing with two types of fairness constraints: a "procedural fairness" which requires the proposed prices to be equal in expectation among different groups, and a "substantive fairness" which requires the accepted prices to be equal in expectation among different groups. A policy that is simultaneously procedural and substantive fair is referred to as "doubly fair". We show that a doubly fair policy must be random to have higher revenue than the best trivial policy that assigns the same price to different groups. In a two-group setting, we propose an online learning algorithm for the 2-group pricing problems that achieves $\tilde{O}(\sqrt{T})$ regret, zero procedural unfairness and $\tilde{O}(\sqrt{T})$ substantive unfairness over $T$ rounds of learning. We also prove two lower bounds showing that these results on regret and unfairness are both information-theoretically optimal up to iterated logarithmic factors. To the best of our knowledge, this is the first dynamic pricing algorithm that learns to price while satisfying two fairness constraints at the same time.