The efficient way to allocate scarce capacity on a flight is to hold an auction as close to departure time as possible. Allocating space prior to that point runs the risk that a ticketed passenger learns that his willingness to pay is lower than he expected (business meeting is cancelled, family member falls ill, etc.) Allocating space close to the time of departure ensures that passengers have resolved any uncertainty about their willingness to pay and those with the highest willingness to pay will be seated.
But with an auction the airline cedes a lot of consumer surplus to the passengers, because in an efficient auction the winner pays not his own willingness to pay, but the willingness to pay of the marginal bidder. The airline is willing to sacrifice efficient allocation in exchange for a mechanism that extracts more of the gains from trade.
The ideal for the airline would be to sell tickets to the auction and to put these tickets up for sale as early as possible, before passengers have any private information about their willingness to pay.
Here’s an extreme example to illustrate. There is a plane with one seat and two potential passengers. By the time of departure they will know their willingness to pay, but when they first enter this world they know only the probability distribution. The airline should announce that there will be a 2nd price auction at the time of departure but in order to be allowed to participate in that auction the passengers must purchase a ticket the moment they are born. The price of this ticket will be set equal to the expected value of consumer surplus from the auction. This way the airline achieves the maximal gains from trade and secures all the rents for itself.
Obviously the problem is that the airline cannot contract with every potential passenger still in the bassinet. Indeed contracting is initiated by the passenger, not the airline. Thus, in order to be able to extract consumer surplus the airline’s mechanism has to give the passengers the incentive to voluntarily contract early prior to the resolution of uncertainty.
A mechanism that accomplishes this will have two features. First, ticket prices must rise as the departure date approaches. This incentivizes early purchases. Second, flights will be oversold. This enables efficient re-allocation of seats on the basis of information realized after tickets are purchased. In particular, those with lowest realized willingness to pay will sell back their tickets in a reverse auction.