Auctions vs Negotiations in Irregular Markets

The classic result of Bulow and Klemperer [BK96] says that in a single-item auction recruiting one more bidder and running the Vickrey auction achieves higher revenue than running the optimal auction with the initial set of bidders, when values are drawn i.i.d. from a regular distribution. However distributions that violate the regularity condition are common and the i.i.d condition is quite restrictive. We give a version of Bulow and Klemperer's result to settings where bidders' values are drawn from non-iid. irregular distributions. The most prevalent reason for a bidder's distribution to be irregular is that the bidder is drawn from a heterogeneous population that consists of several groups of people with different valuation profiles (eg. students and seniors). A bidder drawn from such a population has a distribution that corresponds to a convex combination of the distributions of each population group. Though the individual distributions may satisfy the regularity condition, their convex combination violates it even in the simplest cases. We show that recruiting one person from each group and running the Vickrey auction gets at least half the revenue of the optimal auction in the original setting. Thus without knowing anything about the distribution, if the auctioneer knows that his population consists of several distinct groups, a targeted advertising campaign to recruit one bidder from each population group is nearly as effective as the optimal auction which is complicated to describe and discriminatory. Further, we show that for several natural classes of distributions for the underlying population groups like uniform, exponential, Gaussian and power-law, recruiting just one extra bidder is enough to get at least half of the optimal auction's revenue. Finally, we give the first non-trivial approximations via Vickrey auctions with a single reserve for non-i.i.d. irregular settings.