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Suppose there is an airline that wants to sell 200 seats in a flight. It can either sell them as business class or as economy. Ideally it would sell all as business class, but it is willing to give away seats as economy in case not all can be sold as business class.

Then there is a number of consumer, which all prefer economy seats, but each of them is willing to buy business class in case no economy seat is available.

  • Is this a well-known problem?
  • What is it called?

Edit:

I suppose this is roughly a "game of chicken". But I believe in real markets there will some equilibrium, but I don't know what it depends on.

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  • $\begingroup$ Do you assume that the price of business class tickets as well as that of economy class tickets are unchanging with respect to time? Is time discrete or continuous in your modell? $\endgroup$ – Giskard May 9 '15 at 11:36
  • $\begingroup$ The price may change over time. As for time, I would assume that it is continous. $\endgroup$ – Martin Drautzburg May 9 '15 at 12:21
  • $\begingroup$ I am also uncertain about what you mean when you say they prefer economy seats. Do you mean they that the consumers only care about price and prefer the cheaper kind of seat? (I think economy class does not have any other advantages.) $\endgroup$ – Giskard May 9 '15 at 12:50
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    $\begingroup$ This sounds like a price discrimination problem, except some of your details are a bit fuzzy. If it were a price discrimination problem, the economy passengers would not be willing to buy business seats. As you have it written, it's a bit trivial: the solution is that the airline should sell only 200 seats, because the economy-type consumers are still willing to shell out for business. $\endgroup$ – Shane May 9 '15 at 13:22
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    $\begingroup$ The same is not true for the consumers if there are more than 200 of them, which is probably true. And how can you not know the other players' strategies in equilibrium? $\endgroup$ – Giskard May 25 '15 at 20:17
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If I understand you correctly, all customers prefer economy class to business class (that is, they only care about the lower price).

First, the way you've specified the problem, the airline will always make every seat a business class seat, because if no economy seats are available, the airline will (a) sell the same number of tickets (since customers buy business class if economy isn't available) and (b) sell all the tickets at a higher price.

But maybe you meant something like, fewer people will buy business class seats because the price is higher, so the airline may wish to make some seats economy class so they fill every seat. That is, the airline may initially wish to offer tickets for business class, wait until they stop getting new orders, then lower the price to economy class in order to fill the rest of the seats. Depending on the underlying model of demand and purchasing you may get different results.

I'll highlight one, the 'Coase conjecture', which argues that the sort of pricing scheme I described above will break down because customers rationally anticipate that the airline will lower prices as soon as they stop getting new orders, so they wait for the price to drop.

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The field that considers settings like the one you propose is called revenue (or yield) management. Since the airline deregulation act (1978), this field has become more and more important - also for other industries. Check Chapter 4.5 "Substitutable Capacity" in Talluri and van Ryzin for input on your problem.

What exactly happens in equilibrium depends on the setup. Are there more than 200 consumers? Do they arrive over time or are they present from the beginning? Do all consumers have the same valuations? Are consumers strategic? Myopic? There are many details that potentially drive the model.

Note that the Coase conjecture relies on the assumption that the good is not scarce (less than 200 consumers or additional airplane seats can be produced). If that is what you have in mind, consider this (recent and unpublished, but interesting) paper.

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