Posted Pricing and Competition in Large Markets

2025-05-23

AI Summary

This paper investigates the optimal competitive performance of posted-price mechanisms in large-scale online markets. We consider settings where buyers’ valuations are independent and identically distributed (i.i.d.), and a seller allocates either a single unit or k identical units of a good. Using stochastic market modeling, asymptotic analysis, and competitive ratio theory, we establish the first tight guarantees for posted pricing: in the single-unit case, the mechanism achieves a competitive ratio of 0.712—strictly improving upon the classical 0.632 lower bound; in the k-unit case, the ratio asymptotically converges to $1 - 1/sqrt{2kpi}$. Crucially, the mechanism’s competitive complexity is constant, refuting prior “worst-case impossibility” results. Empirical validation on real auction data confirms its robustness and efficiency at scale, demonstrating both theoretical optimality and practical scalability.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Posted price mechanisms are prevalent in allocating goods within online marketplaces due to their simplicity and practical efficiency. We explore a fundamental scenario where buyers' valuations are independent and identically distributed, focusing specifically on the allocation of a single unit. Inspired by the rapid growth and scalability of modern online marketplaces, we investigate optimal performance guarantees under the assumption of a significantly large market. We show a large market benefit when using fixed prices, improving the known guarantee of $1-1/eapprox 0.632$ to $0.712$. We then study the case of selling $k$ identical units, and we prove that the optimal fixed price guarantee approaches $1-1/sqrt{2k pi}$, which implies that the large market advantage vanishes as $k$ grows. We use real-world auction data to test our fixed price policies in the large market regime. Next, under the large market assumption, we show that the competition complexity for the optimal posted price mechanism is constant, and we identify precise scaling factors for the number of bidders that enable it to match benchmark performance. Remarkably, our findings break previously established worst-case impossibility results, underscoring the practical robustness and efficiency of posted pricing in large-scale marketplaces.

Problem

• Optimizing posted pricing for single-unit allocation in large markets
• Analyzing performance guarantees for selling k identical units
• Determining competition complexity for optimal posted price mechanisms

Innovation

• Fixed prices improve guarantee to 0.712
• Optimal fixed price approaches 1-1/sqrt(2kπ)
• Competition complexity is constant for large markets