Optimal reserve prices under seller uncertainty

Abstract We justify the prevalence of small reserve prices in real-life auctions despite empirical findings that suggest optimal reserve prices in those contexts should be higher. We reconcile such a discrepancy without modifying the standard assumptions about bidders’ preferences, information, or the market environment. Instead, we introduce a form of uncertainty on the seller’s side regarding the distribution of valuations. This uncertainty may arise when the bid sample lacks variables necessary to determine the valuation distribution or when its point estimate differs from the true distribution. We show that the optimal reserve price under uncertainty decreases as the number of bidders grows, and the revenue gain from the optimal reserve price relative to any smaller reserve price—including zero—disappears at an exponential rate. We then show that the reserve price decreases further as the amount of uncertainty, as represented by the integrated variance of the valuation distributions, increases. Finally, we extend the analysis to a risk-averse seller and show that risk aversion reinforces the effect of uncertainty, further lowering the optimal reserve price as the seller trades off expected revenue against revenue volatility.