Doubly Fair Dynamic Pricing (2209.11837v1)

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.

• The paper’s main contribution is the introduction of doubly fair policies that use randomness to balance equal expected prices and payments across groups.
• It develops a novel online learning algorithm achieving ~O(√T) regret while enforcing zero procedural unfairness and bounded substantive unfairness over T rounds.
• Theoretical lower bounds confirm the near-optimality of the approach, highlighting its potential for fair, revenue-optimized pricing in real-world applications.

The paper "Doubly Fair Dynamic Pricing" investigates the challenge of online dynamic pricing under two important fairness constraints: procedural fairness and substantive fairness. Procedural fairness demands that the expected prices proposed to different groups are equal, while substantive fairness mandates that the expected accepted prices, or the prices actually paid by different groups, remain equal as well. The authors introduce the concept of a "doubly fair" policy, which meets both fairness constraints simultaneously.

Key Contributions:

1. Doubly Fair Policies: The paper delineates that any effective doubly fair policy must involve randomness to outperform a trivial policy that assigns the same price to all groups. This is a critical insight, revealing that some form of stochastic approach is necessary to balance fairness and revenue optimization.
2. Algorithm Development: The authors propose a novel online learning algorithm for a setting with two groups. This algorithm achieves:
   • $\tilde{O}(\sqrt{T})$ regret: This denotes the difference between the cumulative revenue of the learned pricing policy and that of a clairvoyant policy, which is optimal.
   • Zero procedural unfairness: Ensuring that the expected pricing among different groups is equal.
   • $\tilde{O}(\sqrt{T})$ substantive unfairness: Ensuring that the expected accepted prices are balanced across groups over $T$ rounds of learning.
3. Theoretical Bounds: The paper establishes two lower bounds indicating that the achieved results regarding regret and unfairness are information-theoretically optimal, up to iterated logarithmic factors. This substantiates the efficiency and theoretical robustness of their proposed solution.
4. First of its Kind: As emphasized in the paper, their algorithm is groundbreaking because it is the first dynamic pricing algorithm designed to learn while adhering to both procedural and substantive fairness constraints.

Implications:

The results of this paper carry significant implications for the design of fair pricing algorithms in online marketplaces. By ensuring that prices are fair in both the procedural and substantive senses:

• It enhances the trust and satisfaction of diverse user groups.
• Balances revenue optimization with fairness, essential for long-term sustainability and regulatory compliance.

Practical Applications:

In practical scenarios, this algorithm can be applied to various industries, such as ride-sharing platforms, e-commerce websites, and other online services where dynamic pricing is employed. Particularly, it can help these platforms avoid biases and ensure fairness in their pricing strategies, thus fostering equitable access and usage across different user demographics.

Overall, the paper makes a substantial contribution to the dynamic pricing literature by establishing a framework for integrating fairness in a methodologically sound manner, while also pushing the boundaries of algorithmic fairness through rigorous theoretical insights.