The economics of flight overbooking (or how to avoid a beating)

The recent news that a passenger was unceremoniously hauled off a United Airlines flight because the airline was unable to persuade enough passengers to voluntarily disembark strikes me as an extreme case of market failure. It is well known that airlines routinely overbook flights in order to maximise the chances of a full aircraft, given that a certain number of passengers will not travel for one reason or another. In the event that there are more passengers than seats, the airline must offer some form of compensation to persuade passengers to voluntarily make way. At the same time, the passenger must weigh up whether the price offered is sufficient to compensate them for the inconvenience. It is a classic bargaining situation worthy of further investigation.

Obviously, the aircraft cannot take off until all passengers are seated and it must wait at the departure gate until the supply and demand for seats is in equilibrium. The airline is charged in proportion to the time elapsed over and above the scheduled departure time. According to industry estimates (here), the cost of such delay is around £70 ($87.50) per minute. The airline will know before boarding begins that they are overbooked so it is in their interests to offer compensation before passengers take their seat, although in the recent United case the airline appears to have waited until they were on board, which is a major strategic error.

We can devise a simple model to analyse the choices facing the airline, based on some arbitrary assumptions but it makes the point. If we assume that it takes 10 minutes to remove luggage and repack the hold, then the airline has an incentive to offer compensation of less than $87.50 up to 10 minutes before the scheduled departure time. Between 9 and 10 minutes prior to departure, the strike price rises to $87.50 which is the price of saving another minute of delay. With less than 10 minutes until the scheduled departure time, and no takers for the offer of compensation, the fine will continue to rise in a linear fashion because the airline cannot unload the luggage and still make the slot. The airline will thus have to raise its offer to passengers on the basis that $87.50 has not proved sufficient incentive so far. On the assumption that one of the passengers does not suddenly “crack” during this standoff, the airline will have to engage in a price discovery process in order to tempt one of them to drop their claim for a seat because otherwise the delay will continue indefinitely.

Suppose that for every minute that elapses, the airline raises its offer by $10. Thus, with 9 minutes to go, the airline will face a fine of $87.50 and offers passengers a similar amount. With eight minutes to go, the fine rises to $175 and the passenger payout to $97.50 and so on (see chart for the representation of the cost structure in this case). The total cost to the airline is the fine levied by the airport for missing the departure slot plus the customer payout (we ignore the costs of any overnight accommodation for inconvenienced passengers). If there are still no takers at the scheduled takeoff time, the airline faces costs of $1052 (a fine of $875 and compensation of $177.50). Obviously, this process could go on for a while – in theory up the point at which it becomes cheaper to refund all passengers and cancel the flight (less the cost of unused fuel and any sundry items).

As it happens, one limit to the process is the legal maximum compensation which US airlines are required to pay ($1350). In our simple model formulation, the airline would have to wait two hours before reaching this limit but by that point the airport fines would exceed $11,000. Indeed, as the chart shows, the airline has an incentive to avoid the steeply rising departure fines. A simpler option would be for the airline to decide in advance how much to offer the passenger before it has to pay any departure fines. Thus, more than 10 minutes prior to departure the airline will not be subject to fines but knows that if it waits until the scheduled departure time before finding an agreement, it will have to pay $1052. The sensible option is thus for the airline to offer the passenger an amount up to $1052 which allows it to take off on time without incurring any departure fines; gains goodwill from the affected passenger and still pay an amount which is less than the legal maximum. Note, by the way, that European airlines are less generous. Payouts per passenger depend on the distance travelled and range from a minimum of €250 for short-haul flights to €650 for longer journeys.

The simple model suffers from a number of shortcomings, none of which change the broad picture. It does not deal with multiple equilibria (i.e. if more than one passenger were to accept the offer). A workaround to this problem is to pick a passenger at random and make the offer rather than hold an auction. More problematic would be the case where the airline needs to bump more than one passenger which changes the airline payoff because different people have different preferences, thus making it harder to find a series of market clearing prices.

This raises a question of what would tempt a passenger to accept the airline’s offer of compensation? It all depends on their time preference, or the rate at which they discount the need to be at their destination on time. This will depend on factors such as income and the value they place on their time. If you are a US worker with just two weeks holiday per year and you lose one day due to flight problems, you may set a high value on the cost of delays. If, however, you earn $50,000 per year, you can earn an extra day’s pay ($200) simply by holding out for two minutes beyond the scheduled departure time.

If the model outlined above does not provide a solution, the process can be short-circuited by the drawing of lots to choose who leaves the aircraft – as apparently United did. Unfortunately, the gentleman removed from the United flight was a doctor, who presumably applied a very high discount rate to his time, so it is hardly surprising that he was not best pleased at being asked to leave the flight – let alone the manner of his departure. There are many issues involved here, but perhaps the key takeaway is that airlines are desperate to avoid departure fines so if you have the time to negotiate, chances are you can drive a hard bargain. There again, you might just be hauled off the aircraft …