If there's one group of executives at this week's Sun Valley media and technology conference who ought to be in good spirits, it's the handful steering the fleet of Internet social networks.

The buttresses of old media institutions, from print to television, are under stress from the advertising downturn, but

social media is thriving as the world flocks to the likes of Facebook, Twitter and LinkedIn.

But the glow of social media is tempered by the hazy business models underlying the Internet's latest trend. The world is talking about Twitter, but as far as anyone knows, the San Francisco-based microblogging site has yet to earn a dime.

So even as Twitter's Evan Williams and Facebook's Mark Zuckerberg were seen conversing with CEOs from Google Inc to DreamWorks Animation SKG Inc and Amazon.com Inc to Dell Inc, there were no signs these talks would soon lead to the deals that have made the Allen & Co conference famous.

Indeed, Rupert Murdoch said Twitter would be a tough investment to justify for News Corp because it has not yet come up with a sustainable way to make money.

Be careful of investing here, Murdoch told reporters.

Sony Corp Chief Executive Howard Stringer was similarly blunt.

A lot of people are doing very well making very little money, he said, when asked about opportunities in social media. That's not a club I'm willing to join.

Early combinations between old and new media, such as News Corp's acquisition of MySpace for $580 million in 2005, offer reasons for caution.

Once the top dog in social media, MySpace's popularity has been overtaken by Facebook. And when MySpace's $900 million advertising deal with Google comes to an end in July 2010, it's not clear what the future holds for the site.

Google CEO Eric Schmidt was coy when asked if he would renew the three-year deal with MySpace at $900 million.

Never say never, he told reporters, but then talked about changes in the marketplace that could affect the terms of any deal. We have more tricks up our sleeve now.

PAID VS FREE

Sales of traditional media staples such as newspapers and DVDs are in a multiyear and seemingly inexorable decline. By contrast, Facebook's active users doubled in eight months to top 200 million in April and U.S. visitors to Twitter surged 83 percent that month over March, according to comScore.

Social media and user-generated content have achieved a level of legitimacy in recent months as people turned to Twitter and Google's YouTube for up-to-the-minute information about major news events such as Iran's post-election protests.

Everybody is talking about Twitter, Liberty Media Corp Chairman John Malone said. It's got wonderful promotional juice because so many celebrities are talking about it and using it.

But he added: It's pretty hard to think of an advertiser base for Twitter, but maybe some creative person will come up with it.

Much of the talk at Sun Valley revolved around whether social media should be free for consumers and supported by advertising, or if a fee-based business model was better.

What is also unclear is whether social networks belong under the roof of Internet companies or traditional media.

Internet entrepreneur Marc Andreessen and others have criticized MySpace under News Corp for focusing too much on selling ads and not enough on innovation.

The issue is how do you continue to run Internet companies as Internet companies and making sure you keep that DNA, said LinkedIn founder Reid Hoffman at Sun Valley.

While News Corp's acquisition of MySpace may not be a home run, Google's $1.6 billion purchase of YouTube shows tech companies have not fared much better -- most analysts believe YouTube operates as an unprofitable unit within Google.

Still, Ironfire Capital's Eric Jackson, a former shareholder of Yahoo Inc, thinks social networks fit better with Web services offered by the likes of Google or Yahoo, than within declining traditional media businesses.

There are questions around the revenue-generating horsepower behind some of these social networking sites, he said. And just kind of bolting on a Twitter to a Viacom or a Time Warner, that's not going to do it.

(Additional reporting by Robert MacMillan and Yinka Adegoke, editing by Tiffany Wu and Andre Grenon)

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