I'm just throwing this out there. Read at your own risk. I don't know what I'm talking about (even more than usual). I'm just thinking out loud, and being ornery. I will explain where I'm coming from after I've made my point.

**There's a difference between "strategic complementarity" and "positive externalities". Strategic complementarity is what creates cities. But cities don't necessarily create positive externalities.** **"Network externalities" is a bit of a BS term that conflates two conceptually distinct things.**

Here's a very simple abstract game to illustrate the difference. (I think I stole this from Cooper and John (pdf).)

All agents are identical. Each agent has a utility function U(x,y), where x is his own action and y is the action chosen by others. In symmetric Nash equilibrium {x*,y*}, where each agent chooses x to maximise his utility taking y as given, and all make the same choice, we know that U_{x}(x*,y*)=0 and x*=y*. (And U_{xx}(x*,y*) < 0 for the second order condition).

**"Strategic complementarity" means U _{xy}(x*,y*) > 0. "Positive externality" means U_{y}(x*,y*) > 0.** Those are different things.

Strategic complementarity means if others do something, that increases your *marginal* utility *of doing the same thing*. Positive externality means if others do something, that increases your *utility*. Period.

**Here's an example with strategic complementarity and a negative externality:**

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