NEW YORK — The online trading platform Robinhood is moving to restrict trading in GameStop and other stocks that have soared recently due to rabid buying by smaller investors.

GameStop stock has rocketed from less than $20 earlier this month to more than $400 today as a volunteer army of investors on social media challenged big institutions who had placed market bets that the stock would fall.

Among the restrictions announced by Robinhood today, investors would only be able to sell their positions and not open new ones in some cases, and Robinhood will try to slow the amount of trading using borrowed money.

Besides GameStop, Robinhood said trading in stocks such as AMC Entertainment, Bed Bath & Beyond, Blackberry, Nokia, Express Inc., Koss Corp. and Naked Brand Group would be affected by the new restrictions.

Some big institutions such as Citron Research and Melvin Capital had placed bets that GameStop shares would fall as the company tries to transform itself from a bricks and mortar retailer to a seller of online video games.

But smaller investors rallied to the stock. By sending the stock soaring higher, they forced the big players to cover their bets by buying the stock, increasing the stock even further.

Robinhood’s stated goal is to “democratize” investing and to bring more regular people into investing. But the company has run afoul of regulators who say the company downplays the risks of trading. Robinhood says it is making moves to better educate users of its platform about those risks.