Why two ice-cream vendors end up side by side: Hotelling's beach
30seconds
Two ice-cream vendors share a long beach, and every swimmer walks to the nearer cart. Where should each one park? Drag the carts and watch the dividing line shift: any step toward the middle steals customers from your rival, so both vendors end up side by side at the centre.
The twist is that the swimmers pay for it. At the centre the average walk is 100 m; at the quarter-points it would be 50 m, with the vendors earning exactly the same. This is Hotelling's 1929 "linear city", and the reason rival shops, petrol stations and even political parties bunch together.
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