[Paper Review] Revenue Optimization in Posted-Price Auctions with Strategic Buyers

Mehryar Mohri, Andrés Muñoz Medina|arXiv (Cornell University)|Nov 23, 2014

Advanced Bandit Algorithms Research13 references3 citations

TL;DR

This paper introduces a novel posted-price auction algorithm, PFS_r, that achieves near-optimal strategic regret—differing from the theoretical lower bound by only a logarithmic factor O(log T), an exponential improvement over prior methods. The algorithm uses a monotonic pricing strategy with adaptive learning, enabling robust revenue optimization against strategic buyers who misreport valuations.

ABSTRACT

We study revenue optimization learning algorithms for posted-price auctions with strategic buyers. We analyze a very broad family of monotone regret minimization algorithms for this problem, which includes the previously best known algorithm, and show that no algorithm in that family admits a strategic regret more favorable than $Ω(\sqrt{T})$. We then introduce a new algorithm that achieves a strategic regret differing from the lower bound only by a factor in $O(\log T)$, an exponential improvement upon the previous best algorithm. Our new algorithm admits a natural analysis and simpler proofs, and the ideas behind its design are general. We also report the results of empirical evaluations comparing our algorithm with the previous state of the art and show a consistent exponential improvement in several different scenarios.

Motivation & Objective

• Address the challenge of revenue optimization in posted-price auctions where buyers act strategically to maximize surplus.
• Overcome limitations of traditional regret definitions in the presence of adaptive, strategic buyers who may misreport valuations.
• Close the gap between existing upper and lower bounds on strategic regret, which previously stood at O(√T).
• Design a simpler, more analyzable algorithm that maintains truthfulness in the limit and improves upon prior state-of-the-art performance empirically.
• Provide a general framework applicable to broader auction mechanisms, including second-price and VCG auctions with strategic behavior.

Proposed method

• Propose a new algorithm, PFS_r, based on a monotonic pricing strategy that adaptively adjusts prices based on observed buyer responses.
• Introduce a parameter r that controls the rate of price increase, with r = log T chosen for unknown γ to achieve logarithmic regret.
• Use a regret analysis framework tailored for strategic buyers, based on the notion of strategic regret introduced by Amin et al. (2013).
• Establish theoretical bounds showing that PFS_r achieves O(T^γ log T log log T) regret for γ > 1/2 and O(log log T) for γ ≤ 1/2.
• Leverage a reduction to discrete bandit problems and exploit structural properties of the game to derive tight regret bounds.
• Validate the algorithm through extensive simulations comparing PFS_r with the monotone algorithm under varying valuations and γ values.

Experimental results

Research questions

• RQ1 Can we design a revenue optimization algorithm for posted-price auctions that achieves sublinear strategic regret against strategic buyers?
• RQ2 What is the fundamental limit of strategic regret in this setting, and can we close the gap between existing upper and lower bounds?
• RQ3 Does a simpler, more analytically tractable algorithm exist that still achieves near-optimal performance?
• RQ4 How does the performance of the new algorithm compare empirically to the previous state of the art under strategic buyer behavior?
• RQ5 Can the algorithm maintain strong performance even when key parameters like γ are unknown?

Key findings

• The proposed PFS_r algorithm achieves a strategic regret of O(T^γ log T log log T) for γ > 1/2 and O(log log T) for γ ≤ 1/2, matching the lower bound up to a logarithmic factor.
• The gap between the best-known upper and lower bounds for strategic regret is reduced from O(√T) to O(log T), representing an exponential improvement.
• Empirical evaluations show consistent and exponential performance gains of PFS_r over the previous state-of-the-art monotone algorithm across multiple valuation and γ settings.
• Even when γ is unknown, setting r = log T yields near-optimal performance, with regret growing as log T, demonstrating robustness.
• The algorithm maintains truthfulness in the limit as γ → 0, a property not satisfied by earlier algorithms.
• The performance of PFS_r remains strong even when the parameter γ is not known, with optimized and unoptimized versions showing comparable results in simulations.