# Hotelling's Law and Differentiation

Imagine there are two ice cream vendors at the beach. They sell exactly the same flavors at exactly the same price. Beachgoers are indifferent, so they walk to whatever vendor is closer.

Where should each ice cream vendor park their stall to maximize the number of customers?

One solution might be for each vendor to serve half of the beach, situating themselves 1/4 from the end (so that nobody has to walk more than 1/4 a mile).

`----A----|----B----`

This might be the "socially optimal" solution, but this rarely happens in practice.

Instead, vendor A could move marginally closer to B, capturing more of their competitor's share while still being closer to customers on their half of the beach.

`-------A-|----B----`

Either A or B can move closer to the middle, capturing more of their competitor's share until they end up right next to each other. That's why you often see a Trader Joe's next to a Whole Foods, a McDonald's next to a Burger King, or two Starbucks across the street from each other.

`--------A|B--------`

The resulting observation is called Hotelling's law – that rational producers will tend to make their products as similar as possible. You can think of this as the opposite of product differentiation. Through the lens of game theory, both A and B have reached Nash Equilibrium by situating themselves in the middle of the beach.

Hotelling's law can be applied to a variety of different situations:

the tendency for political candidates to gravitate towards the ideological center

enterprise software features and differentiation

brand logo design similarity