Optimal internet auctions with costly communication

Iterative auctions can reach an outcome before all bidders have revealed all their preference information. This can decrease costs associated with communication, deliberation, and loss of privacy. We propose an explicit cost model that is inspired by single-item Internet auctions, such as those taking place on auction sites (eBay) or via informal communication (craigslist, mailing lists). A nonzero bid comes at a cost to both the seller and the bidder, and the seller can send broadcast queries at a cost. Under this model, we study auctions that maximize the seller's profit (revenue minus seller cost). We consider multi-round Vickrey auctions (MVAs), in which the seller runs multiple Vickrey auctions, with decreasing reserve prices. We prove that restricting attention to this class is without loss of optimality, show how to compute an optimal MVA, and compare experimentally to some other natural MVAs. Among our findings are that (1) the expected total cost is bounded by a constant for arbitrarily many bidders, and (2) the optimal MVA and profit remain the same as long as the total bid cost is fixed, regardless of which portion of it belongs to the seller and which to the buyer.