what are the economics of overbooking flights?

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Are airlines betting that the last marginal buyer pays so much more than the average cost to convince someone to volunteer to delay their flight?

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There’s a fairly consistent and small percentage of booked tickets that never end up showing to the gate, such as for last minute cancelations, missed connections, etc.

Airlines are aware of these and would rather not fly empty seats while also not selling potential travelers tickets.

**Example math. Not actual numbers.**

Statistically, not everyone makes their flights or and some cancel at the last second.
Airlines know this from thousands of data points.
Say 3 people on average for a given route do not show up, but occasionally everyone does. Say 1 out of 20 flights everyone shows up.
So airlines sell 2-3 more tickets than there are seats on every flight and just bank on a few people not making the flight.
There’s 38-40 more paying customers than if they just let those seats go empty.

On the 20th flight, everyone shows up. The airline offers 2-3x the cost of a ticket for someone to give up their seat.
Sure, it cost them a few tickets worth of money, but as long as it’s not more than the average amount of money gained from making sure every seat has a paying customer in it, then it’s worth.