Picture of Eric SchmidtEric Schmidt is fond of saying that the web isn’t a zero-sum game – that there is plenty of room for two emerging rivals like Facebook and Google to innovate and compete with both growing their revenue.

That’s true enough, although it clearly will be a zero-sum game in a few years, and the winner is surely planning today for tomorrow’s confrontation. Google, for its part, seems to be basing its strategy on the assumption that not everyone will want to join the web platform Facebook is building, and that there is a lot of growth to be found in the web beyond Facebook – that is, the area of the web that Google pretty much controls.

It’s a risky bet, but it seems like the smart one for Google right now. The company has been building social network after social network – Orkut, Buzz, Wave – with mixed results at best. But now it looks like Google has decided to regard social networking as a feature for search. The latest evidence of that approach is in its Tuesday announcement of Hotpot.

Hotpot is a recommendation-driven search engine that relies on a user’s history and Google contacts to suggest restaurants or services intended to appeal to personal tastes. It’s hardly an original idea – it’s pretty clear now why Google badly wanted to buy Yelp. And it faces the same barriers Google has always stumbled over in social networks – there isn’t a critical mass of users at the ready to make it work.

But Hotpot is interesting for another reason: It suggests Google is taking a different approach to social networks. Rather than building an alternative to MySpace or Facebook inside its domain, Google is incorporating social networking into its existing search results, piece by piece.