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Pricing Multi-Unit Markets

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 subadditive valuations over identical items, even in an incomplete-information setting and with uniform prices. We also show that no constant-factor guarantee is possible for general valuations over identical items, even in a full-information setting and with non-uniform prices.