Brexit, at the moment, is an exercise in game theory. This week, both Prime Minister Theresa May and Jeremy Corbyn, the leader of the Labour Party, grudgingly agreed to open the way for options that could help to break the current deadlock over the terms of Britain’s exit from the European Union. In May’s case, the option was a possible vote in Parliament to delay Brexit, which is now scheduled, ready or not, for March 29th; in Corbyn’s, it was a new referendum that might overturn Brexit altogether. Both May and Corbyn were acting because of rebellions within their own ranks, which escalated last week—when both Labour and Conservative M.P.s resigned from their parties—and threatened to spread. May reportedly made her offer because three members of her cabinet were about to quit, taking a dozen junior ministers with them.

On the surface, these concessions should make the prospect of a chaotic Brexit in four weeks less likely. But a great deal of uncertainty remains. Neither May nor Corbyn can necessarily deliver what they’ve offered. Neither even seems to really want to.

An impetus behind the M.P.s’ resignations was the belief that the British government was, as the Dutch Prime Minister, Mark Rutte, put it on Monday, “sleepwalking” toward a cliff edge—the no-deal Brexit. This would mean leaving the E.U. with no agreement in place—no clear rules for trade, for British citizens travelling to Europe, even for things like planes arriving and departing—and, if nothing is done, it will happen on March 29th. May did, in January, present Parliament with a deal that she had negotiated with the E.U., but it was voted down by a historic margin. A no-deal is no one’s preference, although some Tory hard Brexiteers are strangely drawn to it, as if mesmerized by the prospect of Britain standing alone. On Tuesday, May told Parliament, “I believe if we have to we will ultimately make a success of a no-deal.” She was interrupted by jeers and laughter.

Corbyn was the first to bestir himself, when he said, on Monday, that, if Labour’s own vague and unrealistic Brexit plan wasn’t approved by Parliament this week (and it was not), he could see supporting a second referendum. But he also said that he would “continue to push for the other available options”—whatever those may be. In the Brexit referendum, in June of 2016, Labour formally backed remain, but Corbyn didn’t do much to hide his antipathy for the E.U. He had to do something, though. A growing number of M.P.s are fed up with his failure to back a second referendum; with what they see as his toleration of anti-Semitism, which he denies; or, in many cases, with both. (On Wednesday, one of Corbyn’s close allies was suspended, after the Yorkshire Post published a video in which the ally says that the Labor Party has been “too apologetic” about anti-Semitism.)

Corbyn’s commitment might never have been tested, but, on Tuesday, May told Parliament that she was making “three commitments.” The first is another vote on her plan, with whatever tweaks she can get the E.U. to agree on, “by Tuesday, the 12th of March, at the latest.” (There had been rumors in the British press that she might give it a try a week sooner.) If Parliament then votes no again, there will be a vote by March 13th, which will ask members if they would support leaving, as scheduled, with no deal. Their answer should be a resounding no, assuming that everyone is acting rationally—though, when it comes to Brexit, an astonishing number of senior politicians are not. But, assuming that M.P.s vote down a no-deal exit, May will then allow a third parliamentary vote, on March 14th, on whether to ask the European Union for what’s called an Article 50 delay—pushing back the date of Brexit. By then, there will just be two weeks to go.

There are a lot of caveats here. It’s helpful, in mapping them out, to look at the exact wording of May’s “commitment,” which is to

bring forward a motion on whether Parliament wants to seek a short, limited extension to Article 50 and, if the House votes for an extension, seek to agree that extension approved by the House with the EU, and bring forward the necessary legislation to change the exit date commensurate with that extension.

What counts as a “short, limited” time frame? No one knows. Would May impose party discipline to get Tories to vote for the delay? She wouldn’t say. (In the same statement in which she promised the vote on an extension, she said, “Let me be clear: I do not want to see Article 50 extended.”) How about getting it “agreed” by the E.U.? That will be tricky. Each of the twenty-seven other member countries will have to agree to an extension, and any one of them can veto it. A number of European leaders, including Rutte, Pedro Sánchez, of Spain, and Emmanuel Macron, of France, have said that they will agree only if Britain presents an actual plan for what it will do with the extra time; they don’t want to just green-light another season of Brexit psychodrama. (There is a way for Britain to call the whole thing off unilaterally, thanks to a European Court of Justice ruling in December, but to do that it would have to tell the E.U. that it was truly abandoning Brexit, not just playing for time.) And the conditions that they might insist on—Spain has outstanding issues with Britain regarding the status of Gibraltar—could cause Parliament to balk.

For example, May could head to Brussels on March 15th with a mandate to ask for a two-month delay. (That would make a certain amount of sense, since the European Parliament elections are being held from May 23rd to the 26th, and there is a question of whether Britain would participate, if it is still, technically, in the E.U. at that time.) But E.U. diplomats might conclude that two months isn’t enough time to approve another deal, and might instead offer a six-month, or longer, delay, or one with conditions.

A key aspect of game theory is trying to assess your counterpart’s motives. British Brexiteers constantly talk about their conviction that the E.U. will “blink” in the negotiations regarding the question of the border with the Republic of Ireland, which will remain in the E.U.—this involves the so-called backstop. But the U.K. hasn’t actually given the E.U. anything coherent that they can blink at. The problem is that Britain wants both a hard border with the E.U. and a frictionless border with the Republic of Ireland. (Many of the U.K. commitments under the Good Friday Agreement peace accords rely on the openness of that border.) May’s government hasn’t explained how it wants that to happen, beyond dreamy talk about technology that does not yet exist. She has, in the past, rejected the idea of a special status for Northern Ireland, in part because the Tories rely on Northern Irish unionists for their parliamentary majority. So the withdrawal agreement contains the backstop, which means, in effect, that all of the United Kingdom will stay in a customs union, until Parliament comes up with a rational solution. The hard-core Brexiteers want, at the least, a time limit on the backstop—which would allow them to run out the clock. But that would leave Ireland in the lurch: it doesn’t want to undo the Good Friday accords, but it also doesn’t want to compromise its standing in the E.U. The latter concern is the reason that Ireland might even countenance a no-deal Brexit over a bad-deal-for-Ireland one. And yet the British, who have long believed that the Irish can’t do without them, live in the hope that Ireland will abandon the backstop, or that the E.U. will abandon Ireland—something the E.U. has said it will never do.