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As Google’s (s goog) federal antitrust case winds its way through the halls of justice in Washington, investigators for the Federal Trade Commission and the Justice Department will have to consider some fundamental questions about how to apply antitrust law to a company whose primary products are free — and whose monopoly was arguably gained not through coercive relationships but through the power of an algorithm. In other words, what does the word “monopoly” even mean when applied to a web-based entity like Google? Are network effects a barrier to entry, as some have argued, or are online monopolies inherently more fragile than their real-world cousins?

In the last major antitrust case involving a technology giant, Microsoft (s msft) was accused of using its monopoly on computer operating systems to force PC providers to pay for its software even if they didn’t use it, and of other kinds of behavior that crushed competitors and distorted the market. The company eventually settled the case by agreeing to a number of concessions. But the case against Google is a very different one: The company doesn’t actually make anything in the classical sense, and the product it’s best known for — search — is provided to users free of charge, and is paid for by advertising.

As I describe in a new research report for GigaOM Pro looking at the Google case (subscription required), the charges being levelled at the company are twofold. The first charge is that the company has a monopoly on search and on search-related advertising and this gives it an unreasonable amount of control over how content is found online, as well as an ocean of cash generated by those ads. The second allegation is that Google uses the money from its advertising monopoly to develop or buy services that compete with those from other companies, then it uses its control over search to give those services preferential treatment in its search results.

So in the case of Yelp — whose founder and CEO Jeremy Stoppelman testified in a recent Senate hearing regarding Google’s behavior, which wasn’t part of the official FTC investigation but raised many of the same issues — the claim is that when Google couldn’t acquire the company for its local recommendations, it first tried to steal Yelp’s content and use it without asking, then threatened to remove Yelp from Google’s search results altogether and finally bought a competing service called Zagat.

This incorporates almost all the different aspects of the case against Google: the use of its giant cash reserves to try to take over Yelp; the “scraping” of Yelp’s content for use in Google’s own local service, Google Places; the pressure to play by Google’s rules or face deletion from its all-powerful index; and finally, the acquisition of a competitor, to which Google is allegedly giving preferential treatment in its search results. Expedia (s expd) made similar allegations about Google following its purchase of ITA, which provides travel-related information that is used by Expedia and other services (a deal that was reviewed by the FTC).

As I tried to explain in a recent post, antitrust law in the U.S. doesn’t make having a monopoly in a particular market illegal. What the Sherman Act is designed to fight are monopolies that have been achieved through illegal means (i.e., collusion or restraint of trade) and/or monopolies that are being used to harm a particular sector. But it’s even more complex than that. Unfortunately for Yelp and Google’s other critics, it’s not enough just to show that a company with a dominant market position is being unfair to its competitors. It has to be proven that being unfair has some tangible impact on the market, either by restricting choice or raising prices or both.

So Yelp might argue that Google is being unfair by: a) taking its content without asking; and b) giving its own Zagat results a higher ranking in search (assuming it can even be shown that Google is doing this). But does Google’s behavior have any impact apart from being unfair to Yelp? Does it restrict consumer choice when it comes to recommendations services in any real way? And if it does, will consumers have to pay more for those services? Similar questions have to be asked about Google’s dominance in search itself or search-related advertising. Does that dominance affect consumers in a tangible way?

For more on the issues that are confronting investigators as they try to determine whether Google has broken the law or not, please read the full version of my GigaOM Pro report (subscription required).

Post and thumbnail photos courtesy of Flickr users Bloomsberries and Mark Strozier