Bad News Can Be Good News: Early Dropouts in an English Auction with Multi-dimensional Signals

In this note we provide an example of an English auction with multi-dimensional signals, which satisfies the regularity conditions in Milgrom and Weber (1982), including affiliation and monotonicity. However, we demonstrate that a “reversal” may arise: an earlier dropout may be better news to the seller than a later dropout, and the expected revenue can be decreasing over some range of clock prices (conditional on no dropout). Our example suggests that regularity conditions may not aggregate in the analysis of auctions with multi-dimensional signals, and stronger conditions are needed to eliminate the possibility of reversals.