“Privacy,” a disquieting comic-thriller inspired in part by the actions of Edward Snowden, arrives at The Public Theater at roughly the same time a national debate brews over whether Pokémon GO, with its ties to Google, can access too much of a player’s personal information.

Tech embracers -- or, say, anyone with an iPhone -- routinely log bits of data that together provide a glimpse into our intimate lives: finances, locations visited, sexual preferences and so on.

Why worry about Pokémon, “Privacy” leaves you wondering, when we’re clearly doing plenty on our own to strip bare before the world?

Reworked since its London debut in 2014, the collaboration between The Public and Donmar Warehouse centers on an introverted British writer (Daniel Radcliffe, in his fourth New York stage appearance). A painful breakup precedes a move to Manhattan, which he hopes will disrupt his routine. Plus, his ex is here.

Along the way, actors portraying real-world tech, academic and government figures, among them OKCupid founder Christian Rudder and FBI director James Comey, spring to life from the writer’s imagination, both encouraging him to use technology to help form bonds, and warning against it.

“Privacy” relies on audience involvement, guaranteeing no two performances are identical. We’re encouraged to watch with our cellphones on, logged into a dedicated WiFi network. It also features NSA whistleblower Snowden, via previously taped video, in a contribution we can consider his New York stage debut.

Radcliffe, raised almost publicly in the “Harry Potter” films -- and, I'd imagine, obligated to draw boundaries from an early age -- offers another in a line of effacing and affecting performances as the scribe beset by information overload. One effective sequence has him speed-dating with audience “matches” and being forced to admit he lied on a dating profile about his height.

Parts of that scene require the actor to improvise; a second nod for quick-thinking is owed to “SNL” vet Rachel Dratch, here as the writer’s mum and others. The script calls for Dratch to break the fourth wall and discuss metadata tracked by the car service Uber. The night I attended, instructions she provided to examine our own data were rendered obsolete by an app update mere hours before.

Dratch learned about the software update from the audience, yet maintained control over proceedings; Radcliffe shared an explanation during curtain call.

Agreeable supporting performances are turned in by a cast in multiple roles, including De’Adre Aziza, Raffi Barsoumian and Michael Countryman.

The play changes tone in the second act, becoming less about whether the writer can learn to relate to people by relaxing control over information and more about the ways we cede control of data by using our mobile devices. Snowden’s brief participation at the climax plays off an earlier observation that Shakespeare’s “The Tempest” is around the same length as the iTunes user agreement.

There’s something of a British refinement to the proceedings, crafted by co-creators James Graham and Josie Rourke (U.K’s election-night telecast of “The Vote”). I’m not sure any of the revelations come as a jarring surprise, though they raise substantive issues in myriad original ways.

Among them: What's the best balance between security and liberty? When does social media stop helping us stay benignly connected and enable our baser impulses, like stalking? Also—and I’m asking for a friend—is it such a good idea to have every photo you've snapped since 2009 available for public consumption? 

“Privacy” glances off these ideas, concluding finally with the message that it’s good, every so often, to take your phone off the table and have an eye-to-eye verbal confab with your companion, even if it’s about nothing more substantial than your cat.

“Privacy,” through Aug. 14 at The Public Theater, 425 Lafayette St. Tickets: $95 and up. Call 212-967-7555 or publictheater.org.

Follow Robert Kahn on Twitter@RobertKahn