The United Airlines Fiasco: How Game Theory Could Help

United Airlines says it will never again use police to forcibly remove passengers from overfull flights. But this week's public relations disaster for United highlights a problem that airlines face every day: how to entice people to give up their seats voluntarily.

NPR reached out to some of the top thinkers in the world of "game theory" who say they think the industry could be doing a much better job. Here are some solutions they offered.

Treat the problem as a game.

To keep seats full on planes, airlines overbook assuming some people will be no-shows. But when everybody actually shows up, you've got 100 seats on an airplane and you've sold 105 tickets. Sure, it's a problem. But it's also a game.

"Yeah, this is exactly a game theory-type problem," says Joshua Gans, a professor of strategic management at the University of Toronto. "The airline wants some people off the plane; every single person on the plane wants to stay on absent anything else changing."

It's fair to say that United did not play this game very well when the game ended with a passenger being dragged, bloodied and screaming down the aisle.

"Everything should be designed so that that just never happens," Gans says.

Airlines overall actually have already been figuring out how to bump fewer passengers from their flights, though last year it was still about 41,000 people, according to the Department of Transportation. Game theorists like Gans say there are several things the airlines could do to play the overbooked flight game much better.

Don't let passengers board the plane and then take their seats away. And if you do, offer them a lot more money.

"You tend to value something more once you have it," says Kevin Zollman, a philosophy professor at Carnegie Mellon who studies game theory.

There are studies that show that if you show someone a coffee mug and ask them how much they would pay for it, they might offer you $5. But if you instead give the person the same coffee mug and then say, "Hey, I want that coffee mug back. How much will you sell it to me for?" the person is likely to want considerably more money, say $10. And, it's the same thing with airplane seats.

Once people get on a plane and sit down, they think: "Now that's my seat, I'm sitting in it," Zollman says. "So then to ask me to give up my seat would require more." So when airlines offer passengers, say, $800 to give up their seat, that's going to work a lot better in the airport terminal. If passengers are sitting on the plane, the airline should know it needs to offer a lot more money.

Don't make the offer in such a public way, because nobody wants to be a sucker.

Zollman says this is what he's seen most airlines do when they want people to voluntarily give up their seat: "They make this big announcement where they say, 'Would anybody be willing to give up your seat for $400?' " He says the problem with that is that "humans are really sensitive to being suckers."

Zollman says some people would be willing to give up their seat for a $400 ticket voucher. But, he says, "everyone looks around and everyone sees, well, nobody else is doing it, so I must be a sucker if I do it, so I'm not going to do it either."

Analysts say Delta is one airline that's started to ask passengers when they check in whether they'd give up their seat, sometimes asking them how much they would want in exchange. That's a much better approach, Zollman says.

Make better use of technology and start with a big offer.

We get text messages telling us if our flight is delayed. So why not send passengers a text saying, "We are overbooked on your flight; reply to this message if you would give up your seat for a $400 flight voucher."

Zollman says that's a great start. But he says especially when a flight is really overbooked and the airline needs a lot of seats, it could get more passengers in on the game and willing to play if they started with a high offer and worked down from there. He says if the airline texted him and offered $2,000, he'd say yes if he didn't really need to get where he was going on time.

"So now I'm engaged in the process," he says. "Hopefully I'm gonna win it at $2,000." Of course too many people would say yes, so then the airline would offer a lower price. "So now they're bumping it down to $1,500. Well, that's still pretty good; I'll still take that," Zollman says. He says by getting people engaged in the process and active from the beginning, "that would go a long way to getting people to feel like now it's a competition or a game." He says it would likely result in the airlines getting more volunteers and fewer people involuntarily bumped from flights.

Zollman says using games to get out of sticky standoffs can work in lots of other walks of life too. He's written a parenting book about how to use game theory with kids.

Use the information you get from the game to make better choices about who you bump off a flight.

Another advantage to starting with a high offer is that it would give the airlines a key piece of information. People who won't even consider a lot of money in exchange for their seat probably really need to get where they're going. Maybe it's a job interview or their best friend's wedding or they're in a hurry to be with a sick parent who was just admitted to a hospital. Even if the person doesn't scream and get dragged off the plane bleeding, those are passengers you don't want to bump if you can help it.

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