Delta and the Game Theory of Overbooking Flights

Given the deep mess that United Airlines created for itself after a passenger was dragged off a full flight last week, Delta said it could increase the incentives for “voluntary denied boarding.” Agents will now be allowed to offer up to $2,000 to entice passengers to give up their seats, significantly more than the previous limit of $800. If that doesn’t work, the agents’ supervisors can authorize payments of almost $10,000.

Delta’s aim is clear: Use the price incentive to deal with oversold flights and, thus, avoid the social-media-fueled anger that would be sure to erupt again should there be another messy involuntary “reaccommodation” (as United initially called the incident).

On first sight, this approach is likely to work in reducing denied boarding situations for Delta, of which there were an estimated 1,200 in 2016. And once one major airline applies such a system, others are likely to follow (particularly major carriers such as American and United).

But what if insights from game theory -- and, particularly, the greater potential for high collective payouts from credible collaborative collusion -- were to inform passengers’ reactions? They would consider ways to enrich themselves at the expense of the airline.

Here’s an example: Once the airline calls for volunteers, those willing to respond would form a consultative group that would assign one passenger to miss the flight and then agree to collectively hold out until the airlines approaches its new $10,000 maximum. At that point, the one passenger would volunteer, collect the compensation, keep a good portion of it, and make smaller side payments to the other members of the group.

Of course, this is by no means a foolproof approach. Effective collusion and steadfast commitment are tricky for a plane full of strangers, especially when passengers arrive at the gate at different times and, after the flight, are unlikely to interact with their fellow travelers in future. The incentive for any one passenger to refuse to be a member of the group, or break away from it, is considerable -- especially because there are no easy group discipline enforcement mechanisms.

To add to the challenges of forming effective coalitions, the airline compensation is likely to come in the form of travel credits rather than cash, making the side payments complicated and hard to secure. There is also the problem of non-genuine participation by passengers who have no real desire to volunteer, but see this as an opportunity for a potentially risk-free payout.

Even if passengers were to overcome all these problems, such game theoretics are unlikely to allow for a “repeated game,” in which passengers repetitively benefit at the expense of the airline. After all, it wouldn’t take the airline long to realize that its highest net present value approach is now to lower its contingent exposure by reducing the overbooking practices.

Does this mean that Delta’s proposal is nothing more than clever public relations aimed at taking market share away from other airlines. Well, there probably is an element of this, but it's far from a layup, especially as other airlines are likely to follow.

The most probable outcome from this shift in the policy governing voluntary denied boarding is likely to materialize without headline-grabbing news of passengers successfully “arb’ing” the airline. Rather than eye-catching payments, airlines will reduce the amount of seats they sell on oversold flights. And as some passengers will cancel at the last minute, some popular routes may even end up with empty seats.

Passengers will have a slightly less awful experience, airlines will make a little less money, and Twitter storms will focus on other aspects of the travel experience. 

This post originally appeared on Bloomberg View.