Retail clustering

Why do competing shops crowd onto the same street instead of spreading across a town?

If two shops sell the same thing to customers spread evenly through a town, the arrangement that serves everyone best is obvious: put one in each half, so nobody walks far. That is also what you would expect competitors to do — get away from your rival, own your patch. Yet the jewellers are all on one street, the car dealers on one road, the shoe shops in one arcade. Something is pushing them together. What?

Take the simplest version, which is Hotelling's from 1929: a single street a hundred paces long, customers spaced evenly along it, two shops selling the identical good at the identical price. Every customer buys from whichever shop is nearer.

Put shop A at position 25 and shop B at 75. The dividing line is the midpoint, 50. Each takes half the street, and the average customer walks the shortest distance possible. Comfortable — but is it stable? Ask what B gains by moving.

Say B slides down to 60. The dividing line is now halfway between 25 and 60, which is 42.5 — so B serves everyone from 42.5 to 100, which is 57.5 per cent of the street. B has gained purely by moving toward its rival, and lost nothing, because the customers behind B have nowhere better to go. Try 50: the boundary falls to 37.5 and B takes 62.5 per cent. At 30, the boundary is 27.5 and B takes 72.5 per cent.

Do you see the shape of it? Every step B takes toward A moves the boundary by half a step and hands B the customers in between — and the same is true for A. So neither is ever content, and the only pair of positions where neither can gain by shuffling is both shops jammed together at the middle, where each takes exactly the half it had at the start while every customer walks further than before. Both competed hard, neither ended up ahead, and the town ended up worse served.

Is that the whole story? It cannot be, because the prediction fails often enough to be worth taking seriously. So look at what the model leaves out.

The first omission is price. Add price competition to Hotelling's line and the pull reverses: two shops side by side selling identical goods are forced into a price war they both lose, so each would rather keep a distance and enjoy a little local market power. d'Aspremont and colleagues showed in 1979 that under plausible assumptions firms want maximum differentiation. The crowding result is genuine but fragile — it depends on price being fixed or differences small.

The second omission is the customer, and it matters more. Hotelling's customer has already decided to buy and only chooses where. But for some goods — a sofa, a wedding dress, a used car — the whole trip is a comparison. You need to see several before choosing, and you will not make the journey for one shop. A cluster is therefore a bigger draw than any of its members alone: it raises the number of shoppers who come at all. Joining one raises your competition and your footfall together, and for comparison goods the second effect can dominate — which makes clustering cooperative rather than merely defensive.

Both mechanisms are real and they are not rivals. And there is a clean test between them. If clustering were only the marginal-customer fight, it should happen everywhere. It does not: milk, petrol and haircuts are convenience goods, nobody compares three before buying, and those sellers spread out to serve local catchments exactly as the naive intuition predicted. Comparison goods cluster, convenience goods disperse — a pattern the competitive story alone cannot explain.

The Hotelling result is often stated as "competition makes firms similar", and used to explain everything from television schedules to political manifestos. Treat that as an analogy with a specific engine, not a law: it holds where the contested resource is a marginal chooser between two options at the same price, and it weakens or reverses as soon as price, product differences, or the option of not buying are added.

It is also worth separating what the model does and does not claim about consumers. It does not say clustering is bad for shoppers — only that in this setting, where the visit is certain, it adds travel without adding value; where comparison matters, the same clustering is what makes the trip worth making. And a third force sits underneath both: agglomeration proper — shared suppliers, a pool of trained staff, the footfall an anchor creates — which pulls shops together for reasons belonging to neither model, and which is why such quarters persist for centuries.

• How adding price competition to the same line reverses the prediction toward maximum differentiation.
• Why the model has no stable answer for three firms, and what that says about its limits.

Every term the collection defines is gathered in the glossary.