When the Federal Trade Commission (FTC) tries to decide whether to allow of merger of two companies they use the HHI which is the Herfindahl-Hirschman Index. This is calculated by taking all the companies in a particular industry and adding the square of the market share of each company. If a company has a complete monopoly the index is 100*100 = 10,000 (one company with 100% market share). If there are 3 companies with market shares of  50%, 30% and 20% the index is (50*50) + (30*30) + (20*20) = 3800. The FTC looks at what the index would be after a merger. The general rule of thumb is that if the index will be less than 1000 then the merger is approved. If the index will be greater than 1800 then the merger would be blocked or approved only with some changes. If the index is between 1000 and 1800 then the merger will be reviewed and decided on a case by case basis. While this seems pretty straightforward there are sometimes questions about what constitutes an industry. Microsoft tried to argue that they did not have a near monopoly in desktop operating systems because of all the different gaming consoles which considerably diluted their market share…they were overruled.

(The Great Courses – Economics 3rd Edition)