The program for PaperHouse Theatre’s “La Ronde” says it takes place in Vienna at “the fin de siècle” but doesn’t specify which century is ending. Arthur Schnitzler’s play was written in 1897. But the way it’s presented at Duke Energy Theatre, the sexual loopiness could have come from the end of the century that just ended – or be waiting for us at the end of the one we’re in now.

This romantic round-robin connects two characters per scene, in a format that has been adapted for two dozen plays and films. First, a prostitute solicits a soldier in a public park. In the next scene, the soldier comes on to a parlor maid outside a dance hall. Then the parlor maid trysts with a young gentleman in his bedroom.

So it goes. He sleeps with an adulterous wife; she pairs off with her husband, who then cheats on her with a teenager. That girl bewitches a poet, who moves on to an actress, who flirts with a decayed member of the aristocracy, who finally wakes up in the bedroom of the prostitute from scene one.

Schnitzler comments on class and gender roles: The women aren’t exactly victims, but sex is one of their few ways of making a living or asserting independence. (The women with jobs are a whore, an actress – whose social standing wasn’t much higher then – and a maid expected to yield to male employers’ desires.)

He also explores the lunacy of physical infatuation, and that’s the element this cast brings out so well. Sexual fears, vanity, egoism, anxieties and hypocrisies emerge in every scene. “A man can only love where he finds purity and truth,” the husband tells his wife at the end of Act 1. He begins Act 2 in a private room with a giggling teenager whose name he doesn’t know.

Schnitzler has structured the play so the relationships all consist of a new character being controlled by the one we just saw. The prostitute sets the pace for the initial encounter; the soldier asserts himself next; the parlor maid takes control in scene 3, the young gentleman becomes a seducer in scene 4, and so on. The balance of power sometimes changes within a scene, but this overall pattern prevails.

Relationships become more dishonest as the play goes on. The whore wants money, the soldier a quick one in the dark. Then we start to hear about love, but among people who admit what they are. By Act 2, the husband and teenager lie about themselves to each other, the poet makes up a silly false identity, the actress double-talks relentlessly – she’s in the business of taking on false faces, after all – and the aristocrat, an empty suit living out old social conventions, barely knows who or where he is.

This is the first PaperHouse show I’ve seen and the second the company has done. (It was founded last fall to provide opportunities for veteran theater performers outside their normal venues.) It has attracted estimable talent to this show: The male cast offers Chaz Pofahl, Berry Newkirk, Chad Calvert and Matt Cosper; the women include Nicia Carla, Andrea King, Gretchen McGinty and Greta Zandstra.

I was heartened to encounter Michelle Busiek, whom I rarely see onstage, giving a pitch-perfect rendition of a character who is emotionally immature yet sexually precocious, a teenager who has already neglected her mind but learned how to use her body. And it’s good to see Alan Poindexter, who hasn’t acted locally in six years, as the aristocrat, a mournful philosopher whose innocence makes him the most sympathetic character – yet no less a fool for that.