Steven A. Cohen's investment-firm SAC Capital Advisors on Thursday disclosed an increased stake in Zynga Inc., now owning more than 5% of the game maker's shares.

Zynga's shares were up 2.2% to $4.58 in recent after-hours trading. While the stock has risen 18% so far in 2014 through Thursday's close, it is far off the all-time high of nearly $16 in March 2012. Zynga made its debut on the public market in late 2011.

According to a filing with the Securities and Exchange Commission, Mr. Cohen now owns 38.7 million shares, or 5.3%, of Zynga's stock, a stake that includes about 1.7 million shares held by Sigma Capital Management LLC with the rest held by SAC. As of Dec. 31, SAC held 15.8 million Zynga shares.

The increased stake makes Mr. Cohen the largest Zynga shareholder, just slightly above The Vanguard Group's 5.1% stake as of Dec. 31.

Zynga made its name with games like "FarmVille," played on personal computers through a Web browser. Most of the titles were aimed at casual audiences, with themes such as building a farm or playing word games. When the company went public, most of its games were designed for Facebook Inc.'s social network, but within months the company's growth slowed amid a shift of players moving from games on websites to mobile devices.

Zynga earlier this year announced a large acquisition of NaturalMotion to boost a push into mobile, while at the same time cutting deeply among its ranks for the third time in two years.

SAC, meanwhile, is undergoing its own transformation. Last year, SAC agreed to settle criminal charges, pay a fine of almost $1.2 billion and cease managing outside money, which it did earlier this year. Nine current or former SAC employees were convicted on criminal charges related to insider trading. Mr. Cohen wasn't criminally charged.

SAC is being renamed Point72 Asset Management and making a transition into a so-called family office, and as such will manage only Mr. Cohen's personal fortune.

Write to John Kell at john.kell@wsj.com

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