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

TL;DR

This paper develops and analyzes prior-free procurement auctions for multiple units from strategic sellers with capacities, providing tight bounds and new auction mechanisms for various informational settings.

Contribution

It introduces the first profit-maximizing prior-free multi-unit procurement auctions, including PEPA and PEPAC, with proven competitiveness and truthfulness across different seller capacity scenarios.

Findings

PEPA is 4-competitive for unit capacity sellers.

PEPAC is truthful and competitive for non-unit capacities.

Results extend to bi-dimensional private information cases.

Abstract

In this paper, we derive bounds for profit maximizing prior-free procurement auctions where a buyer wishes to procure multiple units of a homogeneous item from n sellers who are strategic about their per unit valuation. The buyer earns the profit by reselling these units in an external consumer market. The paper looks at three scenarios of increasing complexity. First, we look at unit capacity sellers where per unit valuation is private information of each seller and the revenue curve is concave. For this setting, we define two benchmarks. We show that no randomized prior free auction can be constant competitive against any of these two benchmarks. However, for a lightly constrained benchmark we design a prior-free auction PEPA (Profit Extracting Procurement Auction) which is 4-competitive and we show this bound is tight. Second, we study a setting where the sellers have non-unit capacities that are common knowledge and derive similar results. In particular, we propose a prior free auction PEPAC (Profit Extracting Procurement Auction with Capacity) which is truthful for any concave revenue curve. Third, we obtain results in the inherently harder bi-dimensional case where per unit valuation as well as capacities are private information of the sellers. We show that PEPAC is truthful and constant competitive for the specific case of linear revenue curves. We believe that this paper represents the first set of results on single dimensional and bi-dimensional profit maximizing prior-free multi-unit procurement auctions.