Manipulation of public opinion to political ends is nothing new; Satan did it in the Garden of Eden, all sides did it during the cold war. What’s different in the 21st century, as writer Cat Goscovitch’s lie-layering story demonstrates, is the way opinion is manipulated.

This one-woman play is set in Russia in 2016 and centres around a troll factory run by an oligarch whose aim is to disrupt – ideally, destroy – democratic processes: “Today, for the first time, we can use data as a weapon – no guns, no bullets.” Over the course of her monologue, Masha (Rachel Redford) tells us how she, an English literature student at St Petersburg University, came to work for the oligarch, learning to adopt online identities so as to implant ideas into the minds of her Facebook “friends”.

Liz Da Costa’s set of room-size clear boxes set inside one another suggests Russian doll layering. At the heart of this construct is Masha, surrounded by computer screens. The goal, for the team she is part of, is to get people in the UK to vote for Brexit. Masha takes us through the devious means by which she creates opportunities to introduce politically directed hashtags into unrelated exchanges with influencers – #BetterOffOut is one. Chillingly, she shows us how fictions created for the oligarch by psychologists are used to incite racism. Masha believes that her hidden persuasion has referendum-influencing consequences.

This aspect of the play is gripping, pacily directed by Nicolas Kent. Masha’s personal journey from extreme naivety to hardened cynicism is less convincing, though. Although the play is subtitled “a true story”, Masha’s account feels unrealistic, more like a troll-style narrative. The production is strong, Redford’s performance excellent and Goscovitch’s lines crisp, but ultimately A Russian Doll’s multiplicities seem to me to overburden its monologue form.

• A Russian Doll is at the Barn theatre, Cirencester, until 12 June; then at the Arcola, London