Optimal multi-unit combinatorial auctions

The current art in optimal combinatorial auctions is limited to handling the case of a single unit each of multiple items, with each agent bidding on exactly one bundle (single minded bidders). This paper extends the current art by proposing an optimal auction for buying multiple units of multiple items when the bidders are single minded. We develop a procurement auction that minimizes the cost of procurement while satisfying Bayesian incentive compatibility and interim individual rationality. Under appropriate regularity conditions, this optimal auction also satisfies dominant strategy incentive compatibility. The results presented here hold true for equivalent forward auction settings as well. For the two item, multi-unit procurement auction, we design an optimal auction in the presence of the single minded bidders offering volume discounts.