# Pricing Multi-Unit Markets

## TL;DR

This paper analyzes the effectiveness of posted pricing strategies in multi-unit markets with sequential agent arrivals, providing bounds on social welfare guarantees under various informational and valuation assumptions.

## Contribution

It establishes new bounds and insights on the power of posted prices, including constant-factor guarantees for subadditive valuations in incomplete-information settings.

## Key findings

- Uniform prices can guarantee constant-factor social welfare for subadditive valuations.
- Bounds are derived for the maximum welfare achievable with posted prices under different informational assumptions.
- Results compare the effectiveness of uniform versus non-uniform pricing strategies.

## Abstract

We study the power and limitations of posted prices in multi-unit markets, where agents arrive sequentially in an arbitrary order. We prove upper and lower bounds on the largest fraction of the optimal social welfare that can be guaranteed with posted prices, under a range of assumptions about the designer's information and agents' valuations. Our results provide insights about the relative power of uniform and non-uniform prices, the relative difficulty of different valuation classes, and the implications of different informational assumptions. Among other results, we prove constant-factor guarantees for agents with (symmetric) subadditive valuations, even in an incomplete-information setting and with uniform prices.