When the playwrights Joe Murphy and Joe Robertson were looking for ideas for a new production, they stumbled upon a radio show about the negotiations that led to the 1997 Kyoto Protocol.

Some parts of the show, Robertson recalled in a recent interview, made the culmination of those discussions about lowering global carbon emissions sound “like a thriller,” with politicians holding talks in locked rooms and exhausted negotiators falling asleep beneath their desks.

The pair thought that the landmark climate agreement could be the basis for another impactful stage production, similar to “The Jungle,” their hit about a refugee encampment in northern France. The problem was that the negotiations had dragged on for years before the agreement was reached in Kyoto in December 1997 — and that process was at times far from exciting. Most of the action involved representatives from different countries arguing over the language, and even punctuation, they wanted in the protocol.

Climate negotiations “are so bloody boring in one sense,” Robertson said. “The challenge,” he added, “was, ‘How do we do take them, put it onstage and make it dramatic?’”

The playwrights’ answer to that question is “Kyoto,” directed by Stephen Daldry and Justin Martin, and running at the Royal Shakespeare Company’s Swan Theater in Stratford-upon-Avon, England, from Tuesday through July 13.

Almost 30 years after more than 150 nations became party to the Kyoto Protocol, which required some Western nations to cut carbon dioxide emissions, climate change has become an increasingly urgent problem. But the issue is still rarely explored on theater stages.

The few hit plays that have mentioned the subject have often done so only tangentially, including Duncan Macmillan’s “Lungs,” in which a couple deciding whether to have a baby muse about how the state of the planet should influence that decision.

Macmillan said in an email that climate change was “hard to dramatize,” not least because playwrights had to decide whether to include the science underpinning the issue. “You either lose narrative momentum by trying to communicate the science accurately, or you compromise the complexity of the science by keeping the plot moving,” he said.

Robertson and Murphy based “The Jungle” on their own experiences living in a refugee camp in Calais, France, where they built a theater and hosted performances until the French authorities cleared their part of the encampment. For “Kyoto,” the pair had limited knowledge of climate change science or policy, so they spent months researching the negotiations, listening to recordings of the discussions and speaking with dozens of the diplomats and scientists who were present.

A breakthrough came when the playwrights discovered Donald Pearlman, an American lawyer who advised Saudi Arabia and Kuwait in the climate negotiations and tried to get those countries’ representatives to repeatedly delay proceedings.

Murphy said he and Robertson became “obsessed with this agent of disagreement,” who died in 2005, and spoke to his wife and son as part of their research. His story — Der Spiegel, the German newsmagazine, called Pearlman “The High Priest of the Carbon Club” — “unlocked something dramatically for us,” Murphy said.

The playwrights made Pearlman the play’s narrator, and, in “Kyoto,” the audience watches the lobbyist (played by Stephen Kunken) as he tries, and ultimately fails, to upend the negotiations. Murphy compared Pearlman to Iago, the wily soldier in Shakespeare’s “Othello”; there is “always emotion” to watching an antihero, he added.

Even with Pearlman as a focus, Murphy said the pair had to work out how to make the negotiations into riveting theater, and at recent rehearsals in London, the cast and creative team were still fine-tuning some of those details. As they rehearsed a scene in which Pearlman taunts Raul Estrada-Oyuela (Jorge Bosch), the negotiations’ chairman, the cast laughed at Pearlman’s jibes, but afterward Daldry, the co-director, urged the actors to speed things up. “It’s the West Wing, not Ibsen,” he said.

Later, as the actors rehearsed another scene in which negotiators receive a copy of the draft agreement, Daldry suggested the 14-member cast flick rapidly through the documents to give a sense of urgency. “There’s got to be a flurry of paper,” he said.

Robertson, the playwright, said that the team made other choices to help the audience feel involved in the negotiations. Some theatergoers would sit in between the actors around a huge table onstage, as if they were part of the discussions. All attendees would also get a lanyard similar to the ones worn in the actual negotiations.

It was important to the playwrights that “Kyoto” emphasized a moment when governments, against the odds, reached an agreement, Robertson said. “The idea that you could get so many countries to agree about something as complex as legally binding emissions targets was fascinating to us,” he added: “The impossibility of it.”

At a time when disagreement appears to be the norm, as made clear by the war in Ukraine, Murphy said, it “might be a really good idea” to present a play that shows how agreement could come about.

Even if the pathway to agreement involved diplomats’ spending years in locked rooms, arguing over sentence structure.