I consider a package assignment problem where multiple units of indivisible objects are allocated to individuals. The seller can specify additional costs or cost savings on certain packages of objects: e.g., a manufacturer may incur cost savings if they obtain a range of products or services from a single supplier. The objective is to find a socially efficient allocation among buyers. I propose a sealed-bid auction with a novel cost function graph to express the seller's preferences. The graph structure facilitates the use of linear programming to find anonymous, competitive, and package-linear prices. If agents act as price takers, these prices support a Walrasian equilibrium, and I provide additional conditions under which an equilibrium always exists. The auction design guarantees fairness and transparency in pricing, and it admits preferences of the seller or auctioneer over the type and degree of concentration in the market.
Strategic Bidding in Product-Mix, Sequential, and Simultaneous Auctions (Nuffield College Working Paper 2020 - W03)
I study equilibria in Product-Mix, sequential, and simultaneous auctions, which are used to sell differentiated, indivisible goods. A flexible bidder with unit demand, interested in buying any of the goods, competes against several inflexible bidders, each interested in only one specific good. For first-price and second-price payments, I obtain theoretical results on equilibrium bidding, and compare efficiency, revenue, and bidder surplus numerically. Differences in outcomes between Product-Mix and sequential auctions are small for a range of value distributions. The simultaneous auction performs worst in all dimensions, and differences in performance vary substantially with the degree of competition the flexible bidder faces.