> doesn't matter how many players there are. suppose there's one ice cream guy. where is he going to put his ice cream hut? in the center. let's say another one

> doesn't matter how many players there are. suppose there's one ice cream guy. where is he going to put his ice cream hut? in the center. let's say another one shows up. where is he going to put his hut? in the center. the logic repeats. That's not true. Let me explain. In this model (1 dimensional spectrum, be it distance or whatever), if a third player entered the market and the other two players are located at the center then the new players rational choice is to be on either side of the incumbents. He therefore sandwiched the middle player and stole all of his customers, the middle player will then move to the outside and again a player will have been sandwiched. The cycle repeats. But if you add in costs associated with relocating (time or revenue lost or rebranding or moving costs) then this no longer is an effective strategy. A player might realize that this would happen and purposely not locate in the middle in order to avoid a fight. I don't quite remember the solution to a three player model but that was also based on an assumption that there are only three players. It gets highly complicated when there is the possibility of new entrants. The lesson could be watch out for new entrants and stay nimble (so it is cheap for you to react when there are new entrants).