Claude cannot occupy a seat. An airline seat is only used by humans.

If they aren't interested in games they could publish a set fare for a set route. Instead they have 4 or more fare classes visible to end users and more in the backend leading to opaque unpredictable pricing, they gamify the experience using literal points and rewards, they constantly change prices, they charge fees for services that vary depending on fare class, what credit card you purchased the ticket with, what credit card you currently hold, how many times you've flown in the past year, how many miles you've flown, how many dollars you've spent to fly those miles. I'm not sure they could make it more of a game (BTW, games are not in opposition to making money, they frequently enable making more money. Exhibit A is airlines. Game theory textbooks use them as examples).