[scott00]

It depends on what price the auction winners get. If they get the price they bid, it's not optimal. If they all get the price of the most aggressive non-winner it is optimal. It's the difference between a sealed bid first price auction and a sealed bid second price auction. Not sure which way Delta does it.

In practice though, auction theory only works well with high stakes auctions with sophisticated participants (ie, Treasury debt auctions or FCC spectrum auctions). With small stakes and unsophisticated participants, people do crazy stuff, and you need more of a behavioral economics model. (As opposed to a game theoretic model, which is how the standard auction theory stuff works.)

[kelnos]

Why is optimality necessary? (And optimality for whom?) I think all that is necessary is "the people who get bumped feel like they've been compensated fairly".

Unless people blow off the dollar-amount question or later have second thoughts, then people should feel like they've been compensated fairly because they literally told the airline what they believe would be fair compensation. If they provided a bad figure, then really, that's their fault.

If we want to "stick it to the airlines" a bit more and make it equal compensation, then sure, require them to pay all bumped passengers the max bid of anyone who they actually end up bumping. That's not a terrible burden on the airline and is an easy tweak.

[scott00]

Optimality's really never necessary. But it's a good idea sometimes. The two main ways of considering optimality are maximizing revenue and "efficiency". Efficiency is a technical term roughly similar to fairness and the overall good: it tries to measure to what extent auctioned goods go to the participants who most value them.

So going for an optimal auction can be a good idea if you're trying to make the most money possible (many if not most private sector auctions), or to distribute items in an equitable way (lots of government auctions fit this category).

In this particular case, airlines have multiple goals. They want to solve the overbooking for a small amount of money, they want to minimize the time their staff spends dealing with it, and they want to keep their customers happy.

An auction's a good fit for discovering how to keep their customers happy for the least amount of money in an automated way. As to which auction... I don't think theory helps very much here. As I said, theory doesn't work well except in high stakes auctions with sophisticated participants. So you need a behavioral model of your consumers (ie, an understanding of the ways in which they behave irrationally) to figure out a good choice in this case.