SAN JOSE, Calif. — Celebrities, businesses and even the U.S. State Department have bought bogus Facebook likes, Twitter followers or YouTube viewers from offshore “click farms,” where workers tap, tap, tap the thumbs up button, view videos or retweet comments to inflate social media numbers.

Since Facebook launched almost 10 years ago, users have sought to expand their social networks for financial gain, winning friends, bragging rights and professional clout. And social media companies cite the levels of engagement to tout their value.