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Meanwhile Netflix has been steadily losing subscribers to the DVD-by-mail service that first made the company a household name. That’s posed a problem for Netflix because it has been making more money from DVD rentals than Internet streaming because movie and TV studios have been demanding higher licensing fees to deliver their content online.

All those challenges have left Netflix’s stock price more than 70 percent below its peak of nearly $305 a share nearly 16 months ago.

This isn’t the first time that Icahn has taken an interest in a video rental company. He bought a 10 percent stake in Netflix rival Blockbuster Entertainment in 2005 and eventually made his way on to that company’s board. Icahn’s input didn’t seem to help Blockbuster, which eventually filed for bankruptcy protection in 2010 after being outmaneuvered by Netflix and Redbox, a DVD rental kiosk service owned by Coinstar Inc.

Before stepping down in 2007 in a dispute over his compensation, Blockbuster CEO John Antioco openly feuded with Icahn. The acrimony has raised questions whether Icahn’s presence distracted Antioco and other top Blockbuster executives at a time when they should have be spending more of their time focused on the threat posed by Netflix and Redbox.

“We missed a good opportunity there,” Icahn said Wednesday.