Overall, Google (NASDAQ:GOOGL) (NASDAQ:GOOG) continues to be the most dominant search engine in the world, and by a wide amount. For example, data analytics company Net Applications reports Google's desktop search engine market share this year at a massive 63% -- more than three times the second-largest search provider, China's Baidu, which reported 18% during this period. In mobile, Google's demand is unparalleled with a market share of 92%.

However, hidden in these tremendous figures lies a rather uncomfortable fact for Google: Its percentage market share in monetization-heavy desktop search is slipping. For example, in 2013 its desktop search percentage was 77.5% -- 14.5 percentage points higher than its current figure. And while some of that is to be expected, as Google is (mostly) banned in China and the country grows Internet usage, other non-Chinese focused search engines -- most notably, Yahoo and Microsoft's Bing -- have grown market share as well.

Google's facing more than a slipping desktop market share percentage figure, however. While the company is mostly revered in the United States, the European Union has been less enamored with the search engine. A new report has the potential to further strain relations on the other side of the Atlantic.

Focus on the User
A research report published this week concluded Google knowingly manipulates its search results in an attempt to hamper competitors and advantage its own content. The paper is attributed to Michael Luca, Tim Wu, and "the Yelp data science team" and is notable because Wu appears to have had a change of heart in regards to his findings.

The former FTC advisor had written in The New Republic a couple of years ago that Google was (mostly) innocent of anticompetitive practices when the FTC gave the company a slap on the wrist after a lengthy investigation -- even going as far as calling the company "pretty clean." Wu's about-face is noteworthy, although he appears to use a Keynes quote to describe this change: "When the facts change, your thinking should change," he told Re/code.

This can be quite intricate, but on a high-level basis (an even more simplified example is provided below), the latest report co-authored by Wu uses a browser plug-in dubbed "Focus on the User" to search using Google's organic algorithms (sans the alleged content-ranking manipulation) to rank search results with the intention of proving Google was suppressing the most relevant local search results to highlight those that were the best for Google at the expense of users.

And it is important to note Wu's research was paid for and uses the plug-in created by engineers at Yelp and TripAdvisor -- two companies with the most to gain from Google changing its results back to pure organic search. Focus on the User is also the name of an EU effort started by Yelp, Trip Advisor, and others whose home page states that "Google+ is hurting the Internet. Europeans have the power to stop it."

An easier example to understand
If this all sounds like esoteric, inside-baseball-type technobabble, consider the following scenario:

Assume you're a restaurant on an underdeveloped resort island. The only source of entry onto the island is a boat ferry that brings potential customers to a port near your diner hourly. As such, the ferry is of critical value to your success and you invest in ways to better serve this clientele (added shifts, common docks, etc.).

After years of a successful symbiotic relationship, the much-larger ferry company chooses to open a competing restaurant on the other side of the island. Initially you're worried, as competition for limited diners may make life difficult, but you think competition is always in the best interest of the consumer and have existing relationships with long-term vacationers.

Finally, the ferry notifies you it plans to deliver diners to your diner only once a day while bringing vacationers to its new restaurant hourly. Now, substitute Google in for the ferry operator, the ferry itself for search, and Yelp and TripAdvisor for the diner. And while this example is oversimplified, as all examples are, these are the concerns Yelp and TripAdvisor have and essentially what they are alleging Google's doing.

And while nobody knows how the EU might respond to this latest data, as many think Google should be able to manipulate its search results as much as it wants, the union has shown a willingness to take on Big G. And while this report shouldn't change your investing thesis if you own Google, I'd personally keep an eye on the situation.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.