I have written before about letting passengers pay for an empty middle seat next to them and recently about ANZ's cuddle class and related programs which partially implement this.

While I believe airlines could sell the empty middle for somewhere in the range of 30-40% of a regular ticket, this still has issues. In particular, are they really going to bump a poor standby passenger who had a cancelled flight and make them stay another night so that people can get a more comfortable seat?

One idea is to allow the sale of empty middles by dutch auction. In effect this would say, "If there are going to be empty middles on this plane, those who bid the most will get to sit next to them." If this can be done, it's a goldmine of extra revenue for the airline. What they sell costs them nothing -- they are just selling the distribution of passengers on the plane. If the plane fills up, however, they sell it all and nobody is charged.

The dutch auction approach would let each passenger make an offer. If there are 5 empty middles, then the 10 people who sit next to them win, but they all pay the 10th highest bid price. If only 9 passengers bid, the 10th highest price is zero, and everybody pays zero -- which is what happens today, except it's semi-random. While this may seem like a loss for the airline, many game theory tests suggest that dutch auctions often bring the best result, as they make both sides happy, and people bid more, knowing they will actually pay the fair price if they win.

(On the other hand, airlines are masters at having two people pay vastly different prices for exactly the same thing and have managed to avoid too much resentment over it.)

There is one huge problem to solve: How do you arrange that matched bidders are sitting together to share the empty middle? Each empty middle benefits two passengers.

Here are some of the constraints that make this problem hard:

1. If the system isn't simple, people will get confused and there will be customer service costs.
2. Passengers who care about seat comfort are picky, often using sites like SeatGuru to pick seats. They may be really bothered if their seat is moved on them (particularly when they lose the auction) and would dislike not knowing their seat in advance.
3. Airlines will want to maximize revenue, which means having both people sharing the empty middle paying.
4. Passengers will want a sense of fairness. They won't like those who bid not getting a seat when others who didn't bid get one. They actually want everybody to pay if it means those who pay, pay less.
5. On many flights, picky fliers prefer aisle seats, though there are those that prefer windows (particularly on red-eyes.) Either way there can be an imbalance.
6. People should not be worse off after bidding -- for example missing out on getting a whole row to themselves on a lightly loaded flight.

Seats next to N highest bidders are empty, seat-mates luck out

The simplest approach is just to say that the N highest bidders win (and pay the lowest winner's price) and the person in the opposite seat gets a free empty neighbour. If two bidders are in a row, the lower bidder can either pay (good for the airline) or be given a freebie so that they are not treated worse than a person who sat their by accident.

This approach is simple, but may less revenue for the airline. (The real math is complex. With 5 empty middles, the airline earns 5 or more times the 5th highest bid. Or possibly 10 times the 10th highest bid if winners are perfectly paired. It's not impossible for the former number to be higher, particularly if the 10th highest bid is zero.)

Nobody changes seats. Couples and buddies get a nice solution: They need only place one bid and they win their row.

If the airline does not have a system to pair up bidders, those bidders may well build it themselves, since two solos who find one another are well served if they join and pool their bids if one is going to get a freebie.

You do get the annoying result that a row with a $100 bidder and a $1 bidder win over a row with two $90 bidders. One option: If two bidders are in the same row and both win, then both pay half and get equal rights to the space.

The Instructions

The instructions for passengers in this case are reasonably understandable:

1. Pick a seat for yourself next to an empty middle seat, and decide how much you want to offer to keep that seat empty. The minimum offer is $10, but you'll only pay it if it works.
2. As the plane fills up, we'll first fill up the middles next to people who offered less than you, starting of course with those who offered nothing.
3. If we have to fill the seat next to you, you pay nothing (beyond your base ticket.)
4. If you get an empty seat next to you, you and all others who won this pay the amount of the lowest winning offer among you. This is often less than (and never more than) your offer. It is charged to your credit card.
5. If we have more spare middles than there were offers, you are not charged. You only pay when the plane is too full to give everybody who made an offer an empty seat.
6. If you paid, the empty seat is entirely yours to use, as though you bought it, though generally it's nice to let the person on the other side at least stretch their elbows a bit. You can try to charge them half your offer to make more use of it if you wish. If you have a baby on your lap you can seat the baby there. Its underseat storage is yours. You can even invite another passenger to move to it. You can sleep sprawled in two seats, as long as your seatbelt is on. It's up to you.

Attempt to pair bidders

Ideally you want to have two bidders in a row together. Perfectly paired bidders would be matched by bid order, so that the top two bidders are together, and the next two and so on. This maximizes revenue for the airline while providing the best and fairest price to the bidders.

However, perfect pairing is hard. It can be done if people are willing to be reassigned after the auction is conducted (presumably about 90 minutes before the flight.) But many are not willing to tolerate reassignment, particularly in order to give up their chosen seat to a higher bidder when they lost. Some passengers are willing to accept "any aisle" but it's messy. For example, some people love the extra legroom of exits and bulkheads, while others hate the fixed armrests with tray tables included. (Ideal are exit rows with trays in the seat ahead on an extender.) Some care about recline and others don't. Some can't stand being in the open space next to the toilet, some like the room.

As noted, aisles tend to fill up first (at least on daytime flights.) So if bidders want to snap up aisles, you must motivate other bidders to take windows (or vice versa if the balance is the other way.) There has to be a limit on how much imbalance will be allowed before people have to be forced to take a window if they want to be a bidder.

The seatmap can show who is a bidder so that new bidders can pair with them, but this does not pair people with similar bids unless you reveal the bids and only allow pairing for those who match bids. Visible bidding has its own consequences, particularly if changing your bid is allowed.

Whether a row wins can be decided based on the combined bid of the row, or the greater bid of the row. Both have problems. A $100 bidder hardly wants to pair with a $10 bidder in either case, even though both pay the same in a dutch auction. But the real problem comes when one of the bidders wins and the other doesn't. Ideally, the low bidder must be reseated to bring in a winning bidder, but tolerance for that will be low.

Some options:

• Insist that to pair, you must match the partner's bid. People willing to raise their bid may do so, but can't force their row-mate to raise. This effectively makes bids public, however.
• Keep bids secret. High bid wins for the row. Other bidder pays what they bid, or winning dutch price, whichever is lower. People who travel together gain a strong advantage.
• If one party in a winning row loses and the other wins, offer choice: Pay winning amount (even though higher than you bid) or face best efforts reseating to similar seat.
• Try to build a truly usable reseating system. Bidders actually use a UI to map out enough "acceptable alternates" if they must be reseated. Pick enough or face the price/airline-reseat option. This is complex but the complexity is put upon those who seek it. Most people will be happy to move almost anywhere similar (with liftable armrest) if they win, of course.

Public and secret bidding

Having public bids changes the game a lot, too. It might even encourage bidding wars, though bids should never get so high they approach the cost of a business class upgrade, or just plain buying the seat outright. But irrational bidding patterns are common so it might happen. People might get very used to getting that empty middle, and view it as almost as good as business class, particularly in sections like premium economy which have extra legroom.

I tend to think that sealed bids are better than public multi-round bids. Public active bidding is a time-suck, and does not always generate the same results. eBay uses a strange combination of a sealed bid 2nd price auction and a public "increase your bid" auction and it causes much confusion. Though it is certainly the case that people might make one bid (or even have a standard bid in their profile) and when they see the plane filling up to the point that they are sure to lose, desire to increase their bid to get a chance of winning again. This could be very good for the airline, and some of the passengers might think so as well.

Bid with miles & other variants

It's also possible to let people bid with frequent flyer miles, or mixes of miles and cash. Many people have huge banks of miles they never use, which might make the bidding get pretty crazy, and clear up liability for the airlines. While most people tend to view miles as costing about a penny, the airlines always claim they are worth more when they sell or trade them. Allowing a mix would nail that down a bit.

The problem can of course be solved by not having the dutch auction. In that case, each bidder pays what they bid if they win, or perhaps at best pays the next highest bid plus one. In that case if a row has somebody who bid $100 and another who bid $10, the row would win based on the higher bid, and the low bidder would luck out. In this case you obviously need to have the bids be secret. In addition, 2 people who travel together get an obvious advantage, as one bids high and the other bids $1.

Only do this with very similar pools of seats (widebody central seats)

This problem does not exist in the aircraft that have a center column of seats with two aisles. For planes in the 2-X-2 configuration (where X is 3, 4 or 5) this system becomes much simpler, because all those seats tend to be almost identical, with only bulkhead and back-row being different. Here you can even be moving people from row to row fairly safely at the last minute. Most intercontinental widebodies can use this approach, and indeed it's on a long intercontinental where that empty middle is so appealing.

The challenge

Here's a challenge for readers and game theorists. What suggestions can you make to design this system so that:

• Airlines get good revenue but passengers feel they pay a fair price
• It isn't so complex that it causes customer support nightmares and confusion
• Passengers don't find themselves switched unexpectedly into a seat they feel is markedly inferior to the seat they selected

Some thoughts:

• Have the airlines actually work with seatguru to define truly workable classes of equivalence. I'm not sure how much the airlines like seatguru or seatguru-obsessive flyers.
• Airlines tend to like giving an empty middle to parents with a "ride-on-lap" infant, generally at no extra charge though they could easily become bidders, possibly bidders who get a free bid-boost.
• Airlines can do things to please valued passengers, including adding a bonus amount to the bids of people with elite status, or those who paid the most for their tickets. Indeed, a completely alternate approach would be to make it likely that such passengers will always be among the winners if empty middles are to be had. For a while some airlines did promise that the middles next to elite status flyers (or in the premium section) would be the last to be sold.

I should note that I was inspired to write this because tt was pleasant to fly home last night on USAir and get a whole row of 3 coach seats to myself. I mostly fly on United, because it is the big airline for San Francisco, but of late they've been getting too good at filling their planes, and there will often be nothing but middles left, and little chance of upgrade. To my surprise, the USAir flight took 6.2 hours to fly PHL->SFO, an average of 400 mph in an A321. This means considerable fuel saving but I wonder if it means fewer people fly it?

Thoughts?