The Brexit crisis has plunged Remainers and Brexiteers into a dangerous game of the ‘prisoners’ dilemma’

The likely outcome of intransigence on both sides of the Brexit debate is that the judge will send both gang leaders down – so we end up with a bad deal that satisfies nobody

We discovered on Saturday that the government’s Brexit deal is inferior to Theresa May’s rejected deal in three respects: it divides the union by giving Northern Ireland a softer Brexit than the rest of the UK; it relegates our rightfully high environmental and labour standards from legal certainty to mere aspiration; and it only postpones the risk of a no-deal Brexit to the end of the transition period next year.

Within days, we could find ourselves in any one of a variety of positions. We could find Boris Johnson’s deal in law, most likely with an extension beyond 31 October; there could be no agreed deal after the second reading of the withdrawal bill, and no extension to the Brexit process granted by the European Union; there could be agreement to have a confirmatory Final Say referendum; or – as most pundits now predict – we could have general election before Christmas.

But the very fact that all such options are still in play at this late stage is testimony to the total breakdown in trust and compromise in our political system. This breakdown stands in marked contrast to the flexible, yet decisive, way in which the 27 nations of the EU negotiated with Boris Johnson. True, they had the whip hand and got most of what they wanted, but the ability to triangulate between different positions – the essence of doing politics – has become a continental European skill that the British now clearly lack.

At the heart of the present impasse is the classic “prisoners’ dilemma”. Those who saw the film A Beautiful Mind will remember how the Nobel Prize-winning economist, John Nash, developed game theory, of which this thought experiment is an example.

The leaders of two gangs – let’s call them the Brexiteers and the Remainers – are in prison in separate cells, charged with causing a serious punch-up. They know that if they shook hands and reached a compromise (say, a Brexit which keeps the main economic features of the EU but leaves the political) they would get away with a warning and please the neutrals. But they don’t trust the other side and don’t want to risk accusations of “betraying” their own. If Prisoner A, the Brexiteer, sticks to his claim that the other side is solely to blame, and the judge believes him, then he gets off scot-free (a “clean break” Brexit, in this case) but he runs the risk of going down for a very long time (no Brexit at all). Prisoner B has the reverse dilemma: he could stop Brexit altogether, but risks a very hard Brexit (a life sentence) in the process of trying.

The likely outcome of intransigence is that the judge will send both of them down: a bad deal that satisfies nobody.

Though ideas such as retaining a customs union will be floated again, compromise – however desirable at this point – seems unlikely. There will be a battle of political wills, demanding guile and stamina. The first battle is over timetables; the longer the process, the greater the likelihood of scrutiny throwing up problems to be addressed by amendments.

These may be sufficiently numerous and radical that the government no longer has a bill it can sell to its own uncomfortable alliance of the European Research Group, mainstream Tories and Labour Brexiteers. It could then try to trigger a general election. And if the threat of no deal has been neutered by an extension, the opposition is likely to agree to one – even if the outcome is a lottery and may solve nothing.

The bill will also give an opportunity for (mostly) Remainers to secure agreement for a Final Say referendum. The Liberal Democrats and I will be among the supporters of that amendment, but it will only win if there are others who can be persuaded that it is the least worst of several bad options and, as such, the best way out of the Brexit nightmare.

What is absolutely certain is that Brexit will not “get done” any time soon. Even if the bill and the final deal are approved by parliament, there will be another crisis after next summer as the end of the transition period looms in December 2020. With the strong possibility that there will be no sign of a new trade agreement with the EU by then, all the arguments about “clean breaks” and “crashing out” will happen all over again. And again.

There is now a present danger that such a divided country could become split over this single issue indefinitely.

It is perhaps fitting that Brexit has been stuck on the Irish border problem, and the partition that caused it a century ago. A hundred years from now, I fear that arguments over Brexit will still be raging. Unless, somehow, the prisoners learn to compromise.

Vince Cable is the Lib Dem MP for Twickenham and former party leader