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Sergeant Simon Matheson said the men had contacted police in the past two months about a "professional-style operation" in which they were lured to an online platform where they participated in video sex chats.
Unknown to them, the sessions were recorded, and they had subsequently received threats to send money to an offshore account or have compromising images sent to their families.
"The female identifies people they want, then takes them to a separate platform where they chat one-on-one.
"The conversation will lead to acts of a sexual nature that are recorded."
Some of the complainants had paid money, with the amounts depending on what they could afford, Sgt Matheson said.
The payments could not be traced.
"You end up with people in very compromised positions, with professional and personal ramifications."
He expected some victims were too embarrassed to go to the police.
"There are probably more out there."
The initial interactions were on a variety of social media, ranging from widely-used platforms to specialised chat groups focused on activities such as sports and hiking.
He urged people to take precautions with their online activities, and if they were threatened with blackmail, to contact police immediately and not pay any money.
"You cannot trust what you see on the screen at all times."
The Netsafe website had up-to-date information about the latest scams, he said.
Netsafe is an independent, non-profit organisation that provides free support, advice and education about online safety.