εpsilon talk

Musings on math and education. Made with love by the Washington Student Math Association.

Game Theory and Flight Bookings

Have you ever wondered why airlines overbook their flights? Or why don’t they avoid the hassle of turning down a passenger’s flight ticket? The answer to that question lies in a field known as game theory. Game theory is a part of mathematics that deals with strategies to outperform competitors in certain situations. Naturally, airlines want as many passengers as possible on a single flight. This increases the productivity of a single flight as well as gives the airline companies more money.

In the real world, some airlines overbook their flights by over 40 percent! This may seem counterintuitive at first, but, airline companies know this and overbook for a very specific reason. Some people will not board the airplane because they cannot board the flight. They assume that the number of people that will board will be very close to the number of available seats on the airplane. This scenario will give them the most profit. Let’s take a look at this with an example. 

Source: https://www.alaskaair.com/content/travel-info/our-aircraft/737-800

Airline A is offering two flights between two airports, each with a capacity of 100 passengers. Airline A books 100 people on the first flight and 105 people on the second flight, with non-refundable tickets. It is rarely going to be the case that everyone booked for a flight will be able to depart from the airport. Let’s say that 10 people from both flights are unable to get on the airplane. There can be many reasons for missing a flight including becoming sick, earlier flight being late, forgetting something at home, change in plans or being stuck in traffic on the way to the airport. Thus, the first flight will only have 90 people, while the second flight will have 95. Since the second flight has more passengers on board than the first, Airline A makes more profit from the second flight. Note that the numbers used in this example are arbitrary and will not be the same in all situations.

We have seen what happens if the airline ends up underbooking, but what if the opposite occurs and the airline does end up overbooked? In that case, then some passengers will have to wait for a separate flight or will have to receive accommodations from the airline for the delay. Since airlines want to avoid this, they will have to pick the perfect number to overbook their flights to maximize their profits and minimize their costs. This is done by a variety of data samples done by the airline. They overbook flights by a various amount and find which amount gives the airline the most profit. 

Here is another example. Airline A has found out that overbooking by 15% on their flights yields the highest productivity per flight. Each passenger that flies on Airline A gives Airline A a profit of $100, and each passenger that Airline A is forced to cut from the flight makes Airline A lose $250. Each airplane has 100 seats. If Airline A decides to sell 100 seats and all 100 people show up, Airline A makes $10,000. On the other hand, if Airline A chooses to overbook by selling 115 total tickets and 105 show up, Airline A originally makes $11,500 from the 115 tickets sold, but has to pay $1,250 for the five people that won’t fit on the 100 passenger flight. This means that Airline A makes $10,250 in profit. One caveat of this is that those ten people would need to be reassigned to a future flight. Thus, overbooking in this example is better for Airline A. Overbooking can however result in a worse experience for those that were reassigned to a later flight. Once again, these numbers were chosen arbitrarily and will be different for different airline companies. For example, according to Southwest Media’s Corporate Fact Sheet, Southwest Airlines operates more than 4,000 daily departures during peak travel season. This equates to more than 1.3 million flights per year. If we use the numbers from the previous example, Southwest Airlines would make an additional 300 million dollars in profit simply from overbooking!

As we have seen in these examples, strategy is involved in booking airline seats for passengers. While overbooking leaves some customers unhappy, it serves as the best method for airline companies to book more seats. These types of problems are more common than you might think. Game theory has many other applications besides the one we have seen here, including card games like poker and voting in elections of different scales. While it may not seem obvious, there is a little bit of a game everywhere!