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Prerequisites: Chapters 2 and 27.
In Lugano, the hometown of our college, there are two competing shuttle companies that serve the airport in Milano-Malpenso (MXP), which is about 1 hour and 15 minutes away. They have different schedules, but both companies depart from Lugano's railway station. Quite often company A's shuttles are supposed to leave just briefly before company B's. I wondered how many, or actually how few, customers would take the shuttle from company B. Probably only those who arrive at the railway station in the short interval between shuttle A's and shuttle B's departures.
It seems obvious that it matters how the two companies' schedules relate to one another. How should they set up their schedules?
The Simple Model
In our first model we have two competing airport shuttle companies. To simplify things, we assume that the license granting department requires both to schedule four busses per day, one every four hours, each departure at the start of an hour. Thus the only decision left to Ann and Beth, the owners of the shuttles, is at what hour they should start in the morning, 6:00, 7:00, 8:00, or 9:00. By November 1st they must submit their decisions about next year's schedules. So we may model the situation as a simultaneous game.
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