It is in the interests of both players – in this case the UK and the EU – to strike a deal. At the same time, each player has a different view on exactly which deal to strike.

According to the principles of game theory, a player will take action in two main areas to try and secure the best deal for themselves – enhancing their “bargaining power” and improving their “no-deal payoffs”. In other words, they want to be as strong as possible relative to the other player and they want to have attractive outside options.

To date, the UK has not been successful in the first of these areas. Despite considerable posturing from several cabinet members, the UK’s bargaining power remains low. This can be seen by the EU’s ongoing refusal to talk about a trade deal until progress is made on their three “divorce issues”: EU citizens’ rights, the border with Northern Ireland, and the UK’s settlement of its exit bill.

Against this backdrop, Theresa May is entirely correct to turn attention to the UK’s outside options and for her negotiating team to state that it is prepared to walk away without a deal. This is now the best – arguably the only – strategy she has left.

Careful execution

That said, a “no deal is a good deal” strategy needs to be carefully executed, as it is often misunderstood. A frequent misconception is that the greater the UK’s no-deal payoffs (its outside options) appear to be, the more likely the EU will be to offer a good deal. Similarly, many Brexiteers assume that the UK is more likely to walk away without a deal if it takes actions to improve the payoffs it gets from no deal.

Both these views fail to recognise two crucial and interlinked factors. First, the UK’s no-deal payoffs need to be demonstrably greater than any deal the EU is prepared to offer. Second, the UK’s So, what does this mean for the UK’s negotiating team, led by David Davis, and its ability to convince their EU counterparts? To have material impact now, the UK must be seen to commit sufficient resources to a no deal scenario such that the likely payoffs to the UK could imaginably be greater than payoffs from any deal the EU is currently considering. If the UK does this, a rational response from the EU would be to offer a deal that matches the payoffs to the UK in a no deal world. A deal might then be struck.

Unfortunately for the UK, the clock is ticking. Since Article 50 was triggered, there is the deadline of March 2019 to strike any kind of deal. So any pronouncements about future investments also need to be corroborated by actions now to establish the credibility of the UK’s threat to walk away without a deal.

And this is the biggest challenge. Each time one member of the government says that a no deal outcome is “unthinkable”, the credibility of this strategy is undermined. Each time an international trade deal fails to materialise, the credibility of this strategy is undermined further. And each time the Chancellor rejects calls to fund contingency plans for a no deal Brexit, credibility is undermined even more.

The UK’s problem at this stage lies not in a “no deal is a good deal” strategy. The problem lies in the struggle to control these external factors which undermine the credibility of the threat to walk away from negotiations without a deal.

This article was originally published under the title “Game theory experts: credibility is key for a successful ‘no deal’ Brexit strategy” on The Conversation on 18 October 2017.

About the authors:

Abhinay Muthoo is dean of Warwick in London, co-director of the Warwick Policy Lab and professor of Economics, University of Warwick

Siobhan Benita is chief strategy officer for Warwick in London and co-director of the Warwick Policy Lab, University of Warwick