Ex Post Information in Auctions

Abstract

assumptions. Maskin and Riley (1984) show that when the amount a buyer is willing to pay for the auctioned object is not independent of his wealth, expected revenue tends to be lower under open bidding. In contrast, Milgrom and Weber (1982) relax the assumption that valuations are independent and assume instead that buyers' private estimates of the item's value are affiliated. A buyer with a high estimate then tends to believe that other buyers will have higher estimates as well. Maintaining the other assumptions, Milgrom and Weber show that expected revenue is higher in the open ascending bid auction. The intuition behind this result is that in sealed high bid auctions a buyer's bid is determined not only by his own beliefs but, via their bids, by the beliefs of those with lower estimates. A buyer with a low estimate believes that others are more likely to have low estimates as well. He therefore bids less aggressively. It follows that a buyer can beat all opponents who have lower estimates with a bid which is lower than it would be if beliefs were independent.2 Milgrom and Weber also show that if the seller purchases and then publicly reveals information which is positively linked to buyers' valuations, this also raises expected (gross) revenue from an auction. The intuition here is that this helps to reduce the difference in bidders' willingness to pay.3 That such a reduction should raise expected revenue is easily understood for the limiting case in which the seller's information includes all the buyers' private information; for then all buyer asymmetry is eliminated and so expected buyer profit is bid away to zero. The seller therefore reaps the entire surplus. In the following pages the implications of correlated signals are further explored. While Milgrom and Weber emphasized the potential gains to a seller who reveals information ex ante, the focus here is on ex post information. In Section 2 it is shown that, under weak assumptions, the sealed high bid auction is dominated by any auction