On Wednesday, Facebook announced that the F.T.C. had started an antitrust investigation into the company. The Justice Department has also started a broad antitrust review of the technology industry, as have lawmakers. And on Thursday, some state attorneys general met with the Justice Department to discuss competition in the industry.

It is unclear just what role Mr. Hughes, who left Facebook more than a decade ago and has become increasingly critical of Facebook in public, is playing in the pitches to regulators. In the slide presentation, a “Who We Are” page lists Mr. Hughes as the third member of the group. The page concludes with the bullet point, “Speaking only for ourselves, not a client.”

But Mr. Hughes could, for example, provide investigators with leads to current and former company employees and competitors to interview or subpoena. A partly redacted copy of the slides was provided to The New York Times, with names of the people to interview blacked out. Mr. Wu and Mr. Hemphill have shared the redacted version of the slides with some other antitrust experts. One of them, who asked not to be identified, sent it to The Times.

Neither Mr. Hemphill nor Mr. Wu would discuss Mr. Hughes’s involvement, other than to confirm he attended the presentations.

“He has been an important contributor to thinking about these issues,” Mr. Hemphill said.

Mr. Hughes declined to comment, as did Facebook.