The Influence of Privacy Cost on Threshold Strategies in Sealed-Bid First and Second-Price Auctions

This paper follows up on a model described elsewhere by the authors. The model incorporates a privacy cost component to expected payoff in auctions. This is the cost, to the bidder, of the information revealed, by the bid, about the bidder’s valuation. It applies even if the sale is lost, and hence, negative pay-offs, not possible in regular auctions, are possible in auctions with privacy costs. An important concern is whether such a cost affects seller revenue. Our initial analysis of eBay data on sales of the Mustang indicates that those bidders who avail of privacy technology tend to pay a larger sale price, on average, than those who do not. This indicates that privacy cost does effect seller revenue in at least some cases. In this paper we provide a mathematical analysis of threshold strategies where bidders have monotonic increasing strategies for valuations x ≥ xt ≥ 0 and do not bid for valuations x < xt for sealed-bid first and second-price auctions with privacy cost. We observe that bidders pass on at least some, if not all, privacy costs to the seller, and that expected revenues are lower in auctions with privacy costs than otherwise. We also find that a zero-plus bid one arbitrarily close to zero is a valid equilibrium bid, and, in equilibrium, the probability of it winning the auction is non-negligible. Most importantly, we find that when privacy costs are large enough, revenue equivalence does not hold. In such cases, first-price auctions provide higher expected payoffs, but which auction provides a higher revenue depends on the privacy cost function and the number of bidders. Because bidders can choose between the two auctions and revenues and payoffs are not equivalent, and because the bidder passes on at least some of the privacy cost to the seller, it is in the interest of the seller to reduce privacy cost. We conclude that it could often be valuable for the seller to provide privacy-protecting technology while executing an auction, so as to increase revenue by reducing the bidder’s privacy cost.