Impact of second-order uncertainty on the efficiency of the 0.5-double auction

This paper studies the impact of second-order uncertainty on the (ex-post) efficiency of the 0.5-double auction. We consider a discrete double auction model in which the seller’s valuation is either vs or vs and the buyer’s valuation is either vb or vb with 0 = vs < vb < vs < vb = 1. The buyer’s valuation and the seller’s valuation are private information. We further assume that the buyer’s belief about the seller’s valuation is also private information (i.e., there is second-order uncertainty). We show that if vb − vs and vb−vs are sufficiently small, then the efficiency of the 0.5-double auction model with secondorder uncertainty is higher than the efficiency of the 0.5-double auction model with first-order uncertainty. Our result thus serves as an example in which the introduction of higher-order uncertainty results in reducing, instead of increasing, the inefficiency of a bargaining model.