When to Hold an Auction?

Abstract

We study the optimal timing of an auction in a setting where bidders arrive and depart stochastically over time. First, we compare the revenue-maximizing timing and welfare-maximizing timing. We show that sellers hold auctions too late or too early whenever (censored at 0) virtual values are more or less right-skewed than values. We connect the relative right-skewness of virtual values to the “price elasticity of demand” of the bidder’s valuation distribution. In particular, we show that sellers typically hold auctions inefficiently late. Second, we prove that the use of simple timing rules (i.e., a fixed deadline chosen in advance) can lose an arbitrarily large fraction of the revenue from the optimal stopping rule. This underscores the importance of taking timing seriously for good auction market design.