NEW YORK ( TheStreet) Yahoo!'s ( YHOO) chances of a successful and profitable sale for its weary shareholders rests on Google ( GOOG) , Uncle Sam and Facebook.

Yahoo!'s future depends on how much regulators want Google's overall online ad dominance to be challenged and whether as a result of Facebook's emergence, they're willing to say online search and display ad businesses aren't distinct competitive markets. If they are treated as independent markets by authorities, the only Yahoo merger rumor that increases competitiveness against Google is an AOL ( AOL) purchase -- a plan managements rumored to be considering as a growth strategy, but that might take the wind out of a takeover fueled stock surge since August.

The U.S. Department of Justice's record indicates its sometimes looked to build competition against Google even before enforcing usual industry standards of competition. A Google-centric antitrust focus may bode well for Microsoft's ( MSFT) potential Yahoo ambition, especially if Facebook's rise is proof that barriers to overall ad display revenue can be overcome.

In a February 2010 decision, the European Commission and DoJ approved Microsoft's Bing partnership with Yahoo that combined the second and third biggest search competitors. The authorities said the tie up would "increase competition in Internet search and search advertising by allowing Microsoft to become a stronger competitor to Google." The partnership nevertheless made the search market a duopoly between Google and Microsoft, with no third competitor. A similar decision in a potential Yahoo-Microsoft merger would need to show that it increases competitiveness against Google. The only way that happens is if they argue online search and display markets aren't distinct.

The big question is should they be considered separate? "The key point is that a market is something that can be monopolized profitably -- which means that it must include all close substitutes and have significant entry barriers," wrote Roger Noll an antitrust expert and professor of Economics at Stanford University in an email. The idea hinges on whether customers of search ads regard display ads on Facebook and YouTube as a substitute, according to Noll. Do you click on more ads while on Facebook or in Google searches, is there a difference?

Antitrust concerns on a potential Yahoo takeover rose this weekend, when rumors surfaced that Google might finance a Yahoo takeover. The reports also followed speculation that Microsoft would revive its 2007 bid for Yahoo.

There are signs that consumers might not care and substitute freely between search and display ads, signaling that barriers to earnings can be overcome. Consider Facebook's disturbance of status quo. According to eMarketer data of online display ad revenue, Facebook's extected to grow ad revenue by 1000% to nearly $3 billion between 2008 and 2012, almost making it Google's biggest competitor.

In search ad revenue, Google holds nearly an 80% share that would increase if it took over Yahoo and wouldn't be lessened by already partnered Microsoft and Yahoo. Any way you slice it, AOL, is a distant third player with a 1.2% market share. In its Bing partnership, Yahoo sells ads against Microsoft's search results. A Google and Yahoo partnership was nixed on Sherman Antitrust Act concerns in 2008.

In display ad revenue, it's a different story. A merger with Microsoft would actually increase the competitiveness of the market - Yahoo's 13.1% display ad market share combined with Microsoft's 4.8% share would eclipse Facebook's industry leading 16.3% presence. In display ads, Facebook's growth shows consumers aren't wedded to Google, and a potential merger with Microsoft might bolster the competitiveness of Yahoo's top valued display advertising business. In an Oct. 3rd valuation of Yahoo's businesses, Herman Leung of Susquehanna Investment Group priced its display business, home to the worlds largest online news site, at $3.18 a share, its most valuable operation and a key to its $15 valuation.

Taking online ad and display revenue together, a Yahoo and Microsoft merger would actually chip away at Google's dominance in overall online ad revenue. According to eMarketer data for 2011, a Yahoo and Microsoft combination would gain 17.2% of overall online ad revenue from just 6.1% and 11% respectively as independents, a still distant second to Google's $12.8 billion in revenue that accounts for 40.8% of the market.

Additionally, while the overall ad market is growing at 20.2% this year, display ads revenue is growing at 24.5% this year, its also a business where Facebook is expected pace industry growth in 2012. It signals that overall, the online ad market's getting more competitive even if Google's search dominance widens. The problem is that competition would be limited to two or, at best three, companies if Yahoo were bought.

Speaking about the DoJ and the Federal Trade Commission's views on a potential Microsoft takeover of Yahoo, Mark Lemley a professor of antitrust law at Stanford Law School wrote in an email that "Traditionally three-to-two mergers have been considered problematic by the Justice department." Lemley added antitrust authorities, "let through some surprising mergers in recent years, including Ticketmaster- LiveNation ( LYV) and Sirius XM Radio ( SIRI), the challenge to AT&T ( T)- TMobile may suggest that they will once again take that rule seriously."

In online ad revenue, there seems no easy way to get to three competitive businesses. Yahoo and AOL are not growing, and a takeover of Yahoo with a $20 billion market cap by a private equity firm is going to be challenging. "I'm guessing that the size of a merger is such that a private equity firm operating completely alone without a strategic backer is probably a non-starter," said Telly Zachariades a partner at investment bank The Valence Group in a phone interview with TheStreet. Zachariades says that a practical solution might be for a Microsoft or Google to finance a private equity buyout with a non-controlling equity stake. It could allow a new owner to try and grow Yahoo's competitiveness without raising antitrust flags. Such a maneuver could be done in a two-step process where a Microsoft type bidder "funds the deal today and has a call option to buy the balance of the company in the future," added Zachariades. A minority deal might incubate the online ad market's competitiveness before an outright merger proposal is subjected to clearly defined antitrust tests.

In an email to TheStreet, Clayton Moran of The Benchmark Company said, "We do not view Microsoft as the most likely buyer of Yahoo... But if Microsoft were to acquire Yahoo, it could pay a more aggressive price as synergies could be achieved. A Microsoft takeover of Yahoo would likely include a significant anti-trust review."

The question is whether antitrust authorities will consider display and search ads as different markets and what they view as an acceptable way to cultivate industry competition.

After AT&T's ( T) $39 billion merger with T-Mobile was blocked by the Department of Justice in late August, and Express Scripts' ( ESRX) $29 billion takeover of competitor Medco Health Solutions ( MHS) was put through a second review by the Federal Trade Commission in September, it seems increasingly clear that antitrust authorities want to see three strong competitors in an industry for mergers to be approved.

Ultimately, while analysts believe a company sale to a Google or Microsoft might do Yahoo shareholders well, antitrust concerns cast a takeover in doubt, says professor Lemley of Stanford Law School, "the antitrust agencies care about efficiency of supply, but not shareholder interests per se."

-- Written by Antoine Gara in New York