Two ways to auction off an uncertain good

An auction framework is examined where each seller is uncertain about whether or not he will have a good available to sell. A timely example includes the auctioning off of radio spectrum by licensed primary users to unlicensed secondary users. A licensed primary user may not use the spectrum all of the time, but may not know in advance whether or not he will need the spectrum himself and thus whether or not he will have spectrum bandwidth available to rent out. We consider two types of auctions: an ex-post auction which takes place after each seller learns about the availability of the good and an ex-ante auction which takes place before each seller learns about availability. The expected payoffs to buyers, sellers, and to society are then compared. The ex-ante auction can cause buyers to bid on multiple expected units to ensure that they end up with at least one actual unit. Such over purchasing can create a loss to society. Sellers will prefer the ex-post auction since if fewer units are actually available to sell, then they can be sold at a higher price. Whereas in the ex-ante auction all sellers have one expected unit available to sell which results in a lower price. However, if high value buyers are common, then a buyer may prefer the ex-ante auction as it can be easier to win an expected unit than an ex-post actual unit. In contrast, if a buyer has a high valuation and if high value buyers are uncommon, then he may prefer the ex-post auction since he has a strong chance to win an actual unit.