Posted Pricing and Competition in Large Markets

TL;DR

This paper analyzes posted pricing mechanisms in large online markets, demonstrating improved performance guarantees, the impact of multiple units, and the robustness of fixed prices through theoretical results and real-world data.

Contribution

It provides new performance guarantees for fixed prices in large markets, analyzes multi-unit sales, and shows posted prices' robustness, breaking previous worst-case limitations.

Findings

Fixed prices achieve a guarantee of 0.712 in large markets.

The guarantee approaches 1-1/√(2kπ) for selling k units.

Competition complexity remains constant under large market assumptions.

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 $1-1/e\approx 0.632$ 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.