Game Theory, Canada & Brexit

Jonathan Arnott discusses how game theory can explain why a Canada-style deal with the EU may well prove preferable to all in the UK


Long, long ago, in a galaxy not far from here at all, I spent four years at university studying for a Master of Mathematics degree. Much was dry, dull and boring: there’s a limit to the number of partial differential equations I could summon the interest to solve. Every now and again, there was a flash of inspiration: something interesting, elegant, or profound; something able to explain the world in which we live. 

One module was about Game Theory, invented by the brilliant mind of John Forbes Nash Jr. – immortalised not only in the film A Beautiful Mind, but for various mathematical discoveries including the Nash Equilibrium. Like all things Hollywood, the film only partially depicted the reality. Like all pop-science articles on mathematics, I’m going to have to oversimplify a degree-level concept for the sake of readability and word count. 

The ‘Nash Equilibrium’, around which Game Theory is centred, imagines a ‘game’ in which two players have found their best strategy. It doesn’t have to be the ideal outcome, just that it’s never in either player’s best interests to deviate from that strategy. The famous Prisoner’s Dilemma imagines a situation in which two criminals are placed under lock and key. The actions of each player affects the other; if neither confess, they’ll both get a lower sentence on a lesser charge for lack of evidence. Even so, it’s still in both prisoners’ personal interest to confess – in a purely mathematical world, the Nash equilibrium demands that both confess. In the real world, concepts such as ‘not grassing’ are an attempt on the part of criminals to avoid the situation. 

The Prisoner’s Dilemma is remarkably well researched; 40 years ago, over 2,000 academic papers had already been written about it. The same concept applies to nuclear weapons and the concept of mutually-assured destruction, the children’s game of chicken, and interactions between multinational companies. This principle, and more complex ones stemming from it, is found across the world on a daily basis. It predicts and explains human behaviour in many cases.  

For many months, I’ve been wrestling with the question of Brexit. Lacking a crystal ball, I can’t be certain what’s going to happen. I know I’m in favour of Brexit for the many reasons outlined during the referendum campaign (sovereignty, own trade policy, stopping EU courts overruling our own, fishing/farming, control over borders, and saving our EU membership fee). Even if I weren’t in favour of Brexit, I’d be morally and democratically obliged to respect the referendum result – taken in context of the 2014 European elections (won by an anti-EU party), the 2015 General Election (mandating the referendum) and the 2017 General Election (ratifying the referendum). 

Let’s simplify Brexit for a moment to three groups: true/clean Brexiteers, ‘soft’ Brexiteers/Remainers, and EU negotiators. Each of these three groups can veto a deal: clean Brexiteers could bring down the government; soft Brexiteers/Remainers could find the votes to vote down a deal in Parliament, and EU negotiators (or the European Parliament) could vote it down at either European Council or European Parliament. 

The Article 50 clock is ticking. As a simple matter of law, if nothing happens to intervene, the UK will leave the EU at 11pm on March 29th 2019 without a deal. 

The laws of physics tell us that an object in motion will remain in motion unless an outside force (e.g. gravity, friction, another object) acts upon it. The current legal trajectory is towards no-deal (even if those groups would all like to avoid a no-deal scenario). The EU doesn’t consider the Chequers plan better than no-deal. Clean Brexiteers would prefer no-deal to membership of the Customs Union or the Single Market. Soft Brexiteers and Remainers would prefer remaining in the EU, or the Single Market, or Customs Union, to no-deal. 

Each of these proposed options (Remain, Chequers, Single Market, Customs Union) all suffer from the same logical problem: at least one group considers it worse than no-deal. What we’ve seen for the last two years is jockeying for position, with each group trying to persuade the others not to veto their preferred options. 

In Game Theory terms, though, it strikes me that we’ve been asking the wrong questions. The question we should be asking is this: is there a strategy which dominates a no-deal scenario (i.e. everyone would prefer it to a no-deal scenario)? 

I believe there is. Consider a Canada-style free trade deal (or even Canada-plus or Canada-plus-plus as have been described). The EU would rather have a trade deal with the UK than nothing. Remainers and soft-Brexiteers would hate it, but they’d hate it less than they hate a no-deal Brexit. Clean Brexiteers might moan about the financial payments to Brussels, but generally they’d prefer a trade deal to no trade deal – as long as the UK regains its independence in the areas described above. 

I suspect that Juncker, Barnier and Nigel Farage instinctively understand this – an odd trio to mention in the same sentence, but it suggests there’s hope. If there’s any logic to Brexit negotiations, we’re headed for a souped-up Canada deal.  


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