How Auctioneers Set Ex-Ante and Ex-Post Reserve Prices in English Auctions

We compare two commonly used procurement English auction formats - the ex-ante reserve price and the ex-post reserve price, with symmetric and independently distributed private costs. Both formats are indirect implementations of Myerson's optimal mechanism. Both formats yield the same ex post payoffs when auctioneers optimally choose reserve prices. However, the optimal reserve prices follow two counter-intuitive prescriptions: optimal ex-ante reserve prices do not vary with the number of bidders, and optimal ex-post reserve prices are invariant to the realized auction prices. Anticipated regret, Davis et al (2011), and subjective posterior probability judgement, Shachat and Tan (2015), are two different approaches to rationalize observed auctioneers' choices that violate the two counter-intuitive prescriptions respectively. We generalized the latter model to one of Subjective Conditional Probabilities (SCP) which predicts optimal ex-ante reserve prices decreasing in the number of bidders and also predicts optimal ex-post reserve prices increasing in the realized auction prices. In our first experiment, in which costs follow a uniform distribution, we find two possible explanations to the experimental results. First, the auctioneers use the SCP model for both formats. Second, they use format-specific models. In our second experiment with a left-skewed cost distribution, we finally find that the SCP provides a unified behavioral model of how auctioneer set reserve prices in the two formats