A quick game theoretic thought about the Brexit negotiations

In the last few days, I watched the British news a bit about Boris Johnson forming the new UK government. There was of course a lot of talk about the Brexit negotiations. I was a bit puzzled at one point about some of Boris Johnson’s statements. On the one hand there is a lot of talk about being prepared for a hard Brexit and on the other I also heard him say something like that “the chance of a hard Brexit is one in a million” a little while back. So why prepare for some contingency that you do not expect to happen under essentially any circumstances? Also you get the feeling that Boris Johnson, despite having said that, would not so much mind a hard Brexit. In this short post, I explore why all this might actually all make good game theoretic sense (and why perhaps, at least for this matter, his UK opponents should get on board with his strategy if they care about the UK unless, of course, they think they can still stop Brexit).

 

If I understand things correctly, a hard Brexit is something that both negotiating parties (UK and EU) do not really want. Many possible deals would be better for both. However, among these many possible deals, some are better and some are worse for the UK. And the better the deal is for the UK the worse it is for the EU and vice versa (to economics aficionadas: this is because any deal that is contemplated is probably on the Pareto-frontier).  In other words, signing a deal probably offers a surplus to both parties relative to the default option, but it is unclear how this surplus is best divided.

Game theory, in my opinion, does unfortunately not have that much to say about the actual outcome of negotiations. Why do I say this? And please feel free to contest this claim. Well, there are in fact possibly too many game theoretic models of negotiations, all with slightly different assumptions and all with different outcomes. Moreover, I am typically, as in the present case, in no position to judge which of these models is most appropriate for the present case. It is of course possible that a very well empirically informed game theoretic expert on negotiations might be able to do more than I can do here. But do not go away just yet! Ok so it is sadly true that, because of all this, I cannot really predict which deal will eventually be implemented, but I do know something that is useful here and true in essentially all of these models: You are likely to get a better deal the better the default option is for you. So if there is an (inexpensive) way to improve the value of the default option (or threat point as the game theory literature sometimes calls it) you are likely to get a better deal in the end. This is true even if there are no realistic circumstances in which you would really ever end up with the default option. So Boris Johnson, for strategic reasons, may well be right to persist in preparing for a no deal Brexit, while at the same time thinking such an outcome very unlikely.

In a similar vein, it may therefore also be better, for say the UK, to send someone to the negotiations who is well known to think that the default option of a no deal Brexit is not so bad. If the other party believes this, then this maneuver also quite possibly has the effect of getting a better deal for the UK. Such a strategy, however, also has some risks. Suppose that both parties send people to negotiate who are both not too worried about the no deal Brexit scenario. Then, and especially if is unclear how much the two negotiators really value the no deal Brexit scenario, negotiations could break down even if there is a possible deal that both negotiators privately prefer over the no deal Brexit. Because then the uncertainty can lead to negotiators strategically bluffing about how much they value the no deal Brexit, which can lead to a breakdown in negotiations. In fact, it is an implication of the Myerson-Sattherthwaite impossibility theorem that in such cases there is no negotiation / bargaining mechanism in which we can guarantee that negotiators agree to a deal even if there is a deal out there that both would prefer over no deal.

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