Delaying tactics and negotiating Brexit

Late last week, a majority of referendum voters in the United Kingdom chose to leave the European Union. The EU is an association of 28—soon to be 27—countries based on economic and political cooperation. Now we wait until the sides reach a deal on how the UK leaves, but that may not be as simple—or quick—as some say they’d like. Why are both sides delaying the inevitable?

Negotiating Brexit

Viewing London Bridge down a city street

Viewing London Bridge down a city street, by Michael Ash . The UK and EU are both delaying Brexit.

The Treaty of Lisbon, one of the governing documents of the European Union, includes an article detailing how a state can leave the EU. The government of the leaving state must invoke the article. UK leader David Cameron, who supports remaining in the EU, announced he will resign in October as a result of the referendum result, so his government is in no rush to invoke the article.

On the other hand, German leader Angela Merkel—arguably the most powerful person in Europe and the European Union—wants the British government to move first. Instead, she called on the UK to not take too long preparing to leave the EU.

The virtue of delaying

Sometimes actors can benefit from delaying tactics in negotiations, though it runs the risk of causing the opponent to leave the table. Standing firm, as Powell (1996) calls it, presents a trade-off: you can do better as long as the opponent continues the game. Acting nonchalantly may lead your opponent to behave more aggressively if your opponent does not want to wait.

For example, financial advisors recommend staying silent when dealing with a car salesperson. The salesperson needs the commission, and although you want the car, you know you can find another one just like it. Patience may drive the salesperson to sweeten the offer by lowering the price or adding extra options you may not have gotten if you were more hasty to finalize the deal.

A simple delaying game

Think about a simple negotiating game, where two players can choose to either Wait or Act. If both wait, nothing happens, and both players receive the positive status quo, si. If both act, then they receive the individual positive benefit of the deal bi. Waiting while the other player acts results in a deal plus a concession from the more aggressive opponent, such that the one that waited gets bi + c and the one that acted gets bic, where c is the value of the concession. Assume both players want the deal such that bi > si.

Delay Game 1 2
Act Wait
1 Act b1, b2 bcbc
Wait b1 + cb– c s1s2

For this normal form game, we can solve for Nash equilibria. A player will choose to Wait when si > bic; in words, if the concession is too costly relative to the benefit of making a deal, Wait strictly dominates Act; however, if the concession is relatively cheap, such that si < bi – c, you would Act even if you knew your opponent was going to Wait. If concessions are in fact costly, the result is an inefficient outcome (Wait, Wait).

Costly delaying

Let’s complicate this a bit by allowing for waiting to add an extra turn to the game. Waiting can be costly: the value of things decreases over time relative to today: a want a sandwich more now than I want the same sandwich a week from now (we call this discounting the future). In the second turn, waiting imposes a cost θ, and each player can choose to either Deal or No Deal. Choosing Wait, No Deal earns the concession if the other player chooses Act or Wait, Deal.

Delay Game 2 2
Act Wait, Deal Wait, No Deal
1 Act b1b2 b– c – θbc – θ s c – θs+ c – θ
Wait, Deal b1 + c – θb– c – θ b1 – θb2 – θ s1 – θs2 – θ
Wait, No Deal s+ c – θs c – θ s1 – θ, s2 – θ θ, –θ

Because bi > si, we know that Wait, Deal strictly dominates Wait, No Deal for both players, so we can eliminate those strategies. This leaves us with comparing bi + c – θ to bi.

Here we have the opposite consideration as before. In the simpler version of the game, we were concerned with how costly the concession was relative to the status quo; now, we are concerned with how beneficial receiving the concession is relative to the cost of delaying. In other words, if I think you gain more benefit from the concession than the delay costs you, you will wait and make a deal in the future, and so will I, but this means, again, an inefficient outcome: we both choose Wait, Deal in equilibrium when we could have made the same deal today.

Will the UK stay?

Article 50 of the Lisbon Treaty requires that the EU and a leaving country finalize negotiations within two years. This puts us in a situation where the cost of waiting, at least for the next 18 months, is relatively costless compared to the potential concessions. Only in the final months might either side become impatient, but even then, no norm exists for carrying out the article. This further reduces the cost of delaying, despite the rhetoric from Merkel and other EU leaders about a speedy divorce.

At this point, I don’t see the UK backtracking on this, but I do think quite a while—say, a year—will pass before we see any real points of concern in the Article 50 negotiations emerge from either side. Delaying for concessions presents too great an incentive to both sides.

Jeremy L. Wells

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