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In this paper, we derive bounds for profit maximizing prior-free procurementauctions where a buyer wishes to procure multiple units of a homogeneous itemfrom n sellers who are strategic about their per unit valuation. The buyerearns the profit by reselling these units in an external consumer market. Thepaper looks at three scenarios of increasing complexity. First, we look at unitcapacity sellers where per unit valuation is private information of each sellerand the revenue curve is concave. For this setting, we define two benchmarks.We show that no randomized prior free auction can be constant competitiveagainst any of these two benchmarks. However, for a lightly constrainedbenchmark we design a prior-free auction PEPA (Profit Extracting ProcurementAuction) which is 4-competitive and we show this bound is tight. Second, westudy a setting where the sellers have non-unit capacities that are commonknowledge and derive similar results. In particular, we propose a prior freeauction PEPAC (Profit Extracting Procurement Auction with Capacity) which istruthful for any concave revenue curve. Third, we obtain results in theinherently harder bi-dimensional case where per unit valuation as well ascapacities are private information of the sellers. We show that PEPAC istruthful and constant competitive for the specific case of linear revenuecurves. We believe that this paper represents the first set of results onsingle dimensional and bi-dimensional profit maximizing prior-free multi-unitprocurement auctions.

Profit Maximizing Prior-free Multi-unit Procurement Auctions with Capacitated Sellers