The Brexit Negotiations: A Game Plan from Game Theory

The Prime Minister’s Brexit speech on January 17th marked the opening move in the negotiation process that will lead to the UK’s departure from European Union. The UK’s best strategy through these negotiations will depend upon how the other side responds. However, clues are offered by Game Theory, defined as “the study of models of conflict and co-operation between intelligent rational decision makers.”

1. The opening move. Game Theory suggests that the person making the opening move should propose co-operation to arrive at a mutually beneficial solution. The PM’s offer of a “bold and ambitious free-trade agreement” between the UK and her EU partners meets this criterion. Under her proposals, the UK would leave the Single Market, and so regain control over her borders, laws and finances, but continue to offer all EU Member States tariff-free access to British markets, provided they do the same.

2. The response. As demonstrated by The Prisoner’s Dilemma, the EU’s optimal response would be to co-operate. In their initial responses to the PM’s speech, some EU leaders did make positive noises, welcoming the clarity of her approach. However, Game Theory suggests that, unless trust between two parties is high, one party may believe it has more to gain by ending co-operation and pursuing a “beggar my neighbour” policy, advancing their own interests at the expense of the other party. In his Brexit speech on October 7th 2016, President Hollande of France declared that “There must be a threat, there must be a risk, there must be a price.”

3. The principle of reciprocity. Happily for the long-suffering citizens of France, they will shortly be shot of the most incompetent and unpopular President in history of the Fifth Republic. So what he has to say on the subject is irrelevant. What is more worrying is that certain EU leaders have strongly criticised British Ministers for suggesting that Hollande’s approach is not helpful, while refraining from any comment on what he said back in October – suggesting that they agree with his position. Which begs the question – who on earth wants to be a member of any club that threatens to punish them should they decide to leave? However, should the EU adopt Hollande’s policy of vindictive retribution, then Game Theory gives clear guidance on the UK’s response. The very worst response would be to continue to co-operate. Game Theory indicates that the best strategy in the face of threats from the other side is “tit-for-tat”, or “do unto others as they do unto you.” Comments over the past week by the Prime Minister, the Chancellor of the Exchequer and the Foreign Secretary have made it clear that the UK will retaliate against any attempt to “punish” the UK for its temerity in exiting the EU. So, for example, should the EU impose a 10% tariff on UK exports to the single market, the UK should reciprocate by imposing a 10% tariff on any EU imports to the UK.

4. Know your BATNA. The Prime Minister spelt out her BATNA – Best Alternative To a Negotiated Agreement – on January 17th when she stated that “no deal is better than a poor deal”. This is the strongest possible BATNA as it signals that the UK is prepared to walk away, so cannot be held to ransom by the EU. Under this scenario, UK–EU trading relationships would be governed by World Trade Organisation rules, with the UK free to pursue trade deals with the rest of the world on a bilateral basis.

5. Apply leverage and be prepared to “divide and rule”. By referring to security issues in her speech, the PM subtly alluded to the possibility that the UK’s military support to other EU Member States might be compromised if they seek to pursue a punitive policy against the UK during Brexit negotiations. While this has provoked predictable criticism from europhiles, it seems to me to be simple common sense. I can’t think of a single example of a nation giving military support to another nation that is attacking it economically. As the Prime Minister stated, such an approach could not be regarded as that of a friend. And interestingly, after her speech, the President of the EU Council, Donald Tusk of Poland, adopted a notably more conciliatory tone than in some of his earlier statements, or indeed than the views expressed by some of his colleagues from Western European Member States. Could his more moderate approach by any chance have anything to do with anxiety in his native land and the Baltic States about potential threats from the East?

The PM and her Ministers have played their hand well in the first move of the Brexit Game. How it progresses from here depends upon the response of the EU. It is to be hoped that the EU will also enter into co-operative mode, leading to a mutually beneficial Clean Brexit and UK-EU Free Trade Agreement in 2019. However, there is a real risk that negotiations could break down, not because of disagreements between the EU and the UK, but because of fractures within the EU itself. Eastern Members like Poland and the Baltic States may wish to pursue a co-operative strategy but be frustrated by Western Members foolishly seeking to “make an example” of the UK in a misguided attempt to dissuade other Member States from leaving. In that case, the UK’s second best strategy is clear – to leave the negotiating table, cancel subscriptions to the EU, and continue to trade with EU Member States under WTO rules.

In either event, the Prime Minister’s January 17th speech may in time come to be regarded as a case study in the successful application of Game Theory.

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    • James Humphreys on January 22, 2017 at 9:05 pm
    • Reply

    I find your purported game theoretical analysis to be somewhat confused. Here is an analysis of the situation using (Bram’s Theory of Moves.. I think it is fairly self explanatory. The first number in the brackets gives the ordinal preferences of the U.K.; the second gives those of the EU.

    Negotiate Don’t Negotiate

    Demand access (4,1) (3,3)
    to sing. mkt without
    free mov. labour.

    UK GOV

    Accept free mov. (2,4) (1,2)
    labour for access
    to sing. mkt

    The above expresses my view of the the ordinal preferences of the 2 parties.
    That is, 4= preferred option, 3= next best option etc..
    Options for UK are: demand access to single market without accepting free movement of labour and accept free movement of labour for access to the single market. Options for EU are negotiate and don’t negotiate. The first number in the bracket gives the ordinal preference of the U.K. government, the second that of the EU. Thus, for example, (4,1) means the EUs agreeing to negotiate access to the single market without accepting the free movement of labour is the UKs preferred option and the least preferred option of the EU.

    Using backward induction, assuming a starting point of (3,3) with the U.K. moving first we have:
    3,3 3,3 3,3 3,3
    Outcome stay at 3,3

    If the EU moves first:
    3,3 4,1 2,4 3,3
    Outcome 3,3

    Under the rules of Theory of Moves, the outcome is 3,3 whoever moves first, i.e. the UK demands access to the single market without conceding free movement and the EU refuses to negotiate on this basis. Thus, it may be supposed, the the UK ultimately pursues hard Brexit. If this analysis accurately reflects actual ordinal preferences of the actors, May is on a hiding to nothing.

    1. A few comments in response to this very thoughtful analysis.

      Firstly, it is important that we define what we mean by “access to the single market”. Every nation in the world has access to the single market. The analysis would seem to apply to membership of the single market, which requires free movement of labour as part of an overall package including free movement of capital, goods and services. The analysis concludes that membership of the single market without free movement of labour is a nonstarter. Everyone accepts this, including the Prime Minister, who explicitly ruled out membership of the single market in her January 17th speech. What she offered instead was a free-trade deal – i.e., tariff free access of EU member states to the UK market, in a reciprocal arrangement whereby the UK also enjoys tariff free access to EU markets. Your conclusion seems to be that this is also a nonstarter. Well, we shall see. My conclusion is that even if this is rejected by the EU, the UK has a very strong fallback Plan B, in the shape of bilateral free trade deals with other nations – currently prohibited by UK membership of the EU – which could include the USA, Commonwealth countries, and rapidly growing nations in Asia, Africa and Latin America. The gains from these trading arrangements would hugely outweigh any losses as a result of a “worst case” scenario under which the UK only has access to EU markets under WTO rules.

      January 23rd 2017

    • James Humphreys on January 23, 2017 at 6:47 am
    • Reply

    “The opening move. Game Theory suggests that the person making the opening move should propose co-operation to arrive at a mutually beneficial solution. The PM’s offer of a “bold and ambitious free-trade agreement” between the UK and her EU partners meets this criterion. Under her proposals, the UK would leave the Single Market, and so regain control over her borders, laws and finances, but continue to offer all EU Member States tariff-free access to British markets, provided they do the same.”

    Clearly, this *isn’t* seen by the EU as being a “mutually beneficial solution”. As has been widely reported, the EU does not wish to encourage other states to leave it; this might well come about as a result of a generous deal for the UK. So you have simply misunderstood the EU’s preferences here.In game theory it is the actual preferences of the actors which is important, not what a third party thinks their preferences should be.

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