Overbooked Airplanes as Auctions
Airlines often overbook flights, and if everybody shows up then they have no choice but to bump people. They ask passengers to volunteer to give up their seats in exchange for varying amounts of compensation. If they need one volunteer, this is done by asking for volunteers for a small monetary offer (usually a travel voucher), and then gradually increasing the price until someone takes it. However, if there is more than one seat overbooked then it becomes more complicated and can vary by airline. United Airlines has a “uniform” auction policy, where each volunteer gets the airline’s highest compensation offer. On the other hand, American Airlines gives each volunteer only the amount of the offer they personally accepted (1).
The way that the airlines look for volunteers to take these vouchers is quite similar to the concept of auctions that we discussed in class. The only difference is that rather than having the auctioneer sell an item, the “auctioneer” is now attempting to “buy” an item from people competing to “sell” their seat back to the airline. Thus, rather than the player’s payoff being their value minus the price they pay, the player’s payoff is the amount of money they receive from the airline minus their value (how much money they think the hassle of a later flight is worth). In the case of one seat, this is analogous to the “descending bid” auction type. The price goes up until someone takes the offer, and then they get the offered amount of money. Just like a descending bid auction, the best strategy is to accept an offer somewhat above your value, as accepting an offer of your value would yield a payoff of 0 (money received – value). The problem is that there is no perfect method to determine how much above your value you should wait.
If multiple volunteers are needed, then the strategies behind the auctions vary by airline. With United Airlines’ policy, there is an obvious candidate for a dominant strategy. Since you get the maximum payout given to anyone, it makes sense to take the offer when it reaches your value. If we assume that people’s actions aren’t affected by each other (which may be false, but can still be a valuable approximation), then this would be a dominant strategy. You will receive as much money as the other bidders let it get up to, so it makes sense to get in as soon as it’s “worth it” to you, and the final price will be determined by how high the other bidders let it go (which would have been the same whether or not you decided to take the earlier offer, much like a second-price auction). On the other hand, under American Airlines policy you only receive as much money as the offer you accept, regardless of if other passengers get more. Thus, it is no longer a good strategy to accept the offer at your value, as it will give you a payoff of 0. You must try to wait for the compensation to be higher than your value, much like a first-price or ascending bid auction.
Kevin Zollman, a professor at Carnegie Mellon University, believes that airlines could use game theory to create better methods for running these “auctions,” such that more people volunteer and there are fewer situations requiring involuntary bumping. He suggests that the compensation starts high and then decreases gradually until there is only one (or however many volunteers are needed) left, and they receive what the offer is currently at (2). The main advantage of this approach is that people will be engaged from the beginning (many more people will say yes to an absurdly high value), which can speed up the process immensely as they are now considering the option of taking a later flight more than they would’ve otherwise. Also, note that the strategy for this game is very similar to that of United Airlines’ policy. This auction is analogous to the ascending bid auction, which was shown in class to be strategically equivalent to the second-bid auction. In other words, it’s a dominant strategy to stay in until the compensation falls below your value, and then drop out. This could provide an additional benefit for the airlines; for those not well-versed in game theory, games with a dominant strategy are by far the easiest to understand. This may lead to more passengers choosing to participate, as there is less uncertainty. Again, this would decrease the number of involuntary bumpings that the airline must do, which is much better for their public relations.
Sources:
(1) https://news.wttw.com/2017/05/08/flight-overbooked-use-game-theory-get-biggest-payout
(2) https://www.npr.org/2017/04/13/523726313/how-game-theory-relates-to-airline-booking