The US threat of trade sanctions has put the EU in a difficult position. Nevertheless, the EU must respond decisively – not just to protect its own interests but those of the multilateral trading system, and to demonstrate to the US and other partners that trade is not a zero-sum game.









The threat of trade sanctions, via direct tariffs or the breaking of the Iran deal, is an act of diplomatic aggression the like of which we have not seen in a long time.

Who wins when the US takes such a stance? Will America be great again? And how should the EU – the greatest (de facto) economic and diplomatic ally of the US – respond to this ‘invitation’ to what I believe to be a ‘game of chicken’? Let me explain why I view the current situation this way and why the EU should study closely what such a game portends before reacting.

Two parties, the US and the EU, engage in trade with each other. While this is not equal to world trade, it is very relevant for world trade given their size. If they both comply with international law that promotes free trade, they have access to big markets which they split.

If one of them decides to impose trade sanctions, such as tariffs, then they capture a bigger share of the market by prohibiting imports, provided these sanctions are unilateral. If both parties impose sanctions, trade collapses. Both parties lose a lot. The pay-off matrix looks as follows:

Table 1: Matrix of Pay-outs

EU

US Cooperate Sanction Cooperate 1 , 1 0 , 2 Sanction 2 , 0 -10 , -10

Note: red numbers are pay-offs for the US and blue numbers are pay-offs for the EU.

The numbers here are neither representing real economic values, nor reflecting true preferences. They are chosen to indicate that:

The ‘good’ outcome for both parties is when countries trade with each other (1,1);

yes, there is an incentive to deviate from the agreements – but only provided the other does not: (2,0) or (0,2); and

The worst outcome is really very bad, as it makes trade collapse (hence -10, -10 and not just, say, -1, -1).

What is interesting about this game is that the ‘good’ outcome, (1,1), is not immediately attainable. The fact that we all agree 2 is bigger than 1 implies that both parties would prefer to achieve 2, if they possibly could. What is not so obvious is how to get there, as for one partner to achieve 2 the other must achieve 0, and that is not desirable. In other words, for the US to gain from imposing sanctions, the EU must not retaliate. The EU however, and given its own payoffs, might think otherwise.

A way of moving away from this possibly indeterminate outcome is by looking for likely actions, instead of actual ones. This is equivalent to moving from what is called pure-form strategies to mixed ones. In the appendix to this blog, I derive the likelihood with which either party is going to cooperate or impose actions.

I show that, given the numbers in Table 1 that I have arbitrarily chosen, both partners recognise that they should Cooperate 10 out of 11 times and impose Sanctions only 1 out of 11 times. In other words, despite their desire to get to 2, they also recognise that -10 is a really bad outcome and therefore should be avoided as much as possible!

In Table 2, then, I calculate how often the four different outcomes might occur.

Table 2: Mixed strategies, matrix of probabilities

EU

US Cooperate Sanction Cooperate ( 10/11 )* ( 10/11 )=100/121 ( 10/11 )* ( 10/11 )=10/121 Sanction ( 1/11 )* ( 10/11 )=10/121 ( 1/11 )* ( 1/11 )=1/121

Notes: probabilities add up to one to exhaust all possible outcomes.

Here is what the game predicts:

The good outcome is the most likely outcome (100/121). And this probability is big! In other words, countries cooperate and they do so almost all the time. This is a very important prediction. Countries do recognise that respecting agreements is beneficial and they pursue that course, even if there are incentives to deviate.

And this probability is big! In other words, countries cooperate and they do so almost all the time. This is a very important prediction. Countries do recognise that respecting agreements is beneficial and they pursue that course, even if there are incentives to deviate. The bad outcome is a very unlikely outcome (1/121). This follows naturally from the first point. We do not resort to mutual sanctioning because we realise that the losses for all are enormous.

This follows naturally from the first point. We do not resort to mutual sanctioning because we realise that the losses for all are enormous. However, the bad outcome is not a zero-probability outcome. This is how sanctions work! You need to have the threat of sanctions to impose discipline, but they need to be applied as rarely as possible or everybody loses . We need however, to appreciate the fact that this outcome is not totally eliminated.

This is how sanctions work! You need to have the threat of sanctions to impose discipline, but they need to be applied as rarely as possible or everybody loses We need however, to appreciate the fact that this outcome is not totally eliminated. Lastly, either party may achieve its most preferred outcome (2,0 or 0,2). So, temptation to deviate exists, but again this is a small probability event (10/121 times two).

If this game were played repeatedly, (which, of course, it is) a player would gain an advantage from getting a reputation for being aggressive. However, if both players adopt such a strategy, the outcome is very destructive.

But let’s walk through this argument further. Mr. Trump has gone out of his way to argue that open trade has been damaging to the US and that restricting it would help protect US interests. How does the matrix of pay-offs change?

The US announces that it will impose sanctions. In the language of the game it is equivalent to saying that the US has very little to lose by doing so. The pay-offs are now asymmetric in favour of the US. This means that their loss is much smaller, by comparison to that of the EU, when the bad outcome arises.

The logic of this threat can be captured by reducing the losses that the US has in the very worst outcome (i.e. less to lose: from -10 to -1). The table of pure form pay-offs can then be described as follows:

Table 3: Matrix of Pay-outs with current US trade policy

EU

US Cooperate Sanction Cooperate 1 , 1 0 , 2 Sanction 2 , 0 -1 , -10



Note: red numbers are pay-offs for the US and blue numbers are pay-offs for the EU.

How likely are the two countries to pursue either of the two options now? I show in the appendix, the EU now imposes sanctions 1 out of 2 times! Compare that to 1 out of 11 times in the previous game. The fact that the US has declared that it has very little to lose, has forced the EU to impose sanctions a lot more often than otherwise.

In other words, the EU is now pursuing the ‘wrong’ strategy a lot more often than previously and has become an ‘aggressor’ itself. By implication, the possibility of world trade collapsing is very real and no longer a very unlikely outcome.

Interestingly, the US still pursues its policies with the same probabilities as before.

Table 4: Mixed strategies, matrix of probabilities with current US trade policy

EU

US Cooperate Sanction Cooperate ( 10/11 )* ( 1/2 )=10/22 ( 10/11 )* ( 1/2 )=10/22 Sanction ( 1/11 )* ( 1/2 )=1/22 ( 1/11 )* ( 1/2 )=1/22

Note:probabilities add up to on to exhaust all possible outcomes

Here is a summary of how the game has now changed:

The good outcome occurs now less than half of the time (10/22)! This is a very big reduction when in the previous game it was a very likely outcome (100/121). Free trade (Cooperative outcome) is therefore now less likely than the other alternatives combined.

This is a very big reduction when in the previous game it was a very likely outcome (100/121). Free trade (Cooperative outcome) is therefore now less likely than the other alternatives combined. The EU forces the US to cooperate by sanctioning more often (10/22). That is, of course, the reason for the EU Sanctioning. So, the EU gets the 2 more often than previously.

That is, of course, the reason for the EU Sanctioning. So, the EU gets the 2 more often than previously. However, free trade ends a lot more often too! The probability of everyone sanctioning is now 1 out of 22 when it was 1 out of 121 previously. This is the definition of an escalation!

The game of chicken predicts that as the opponent becomes more aggressive, retaliation is the only way to stay in the game – and all the more so as the opponent becomes more aggressive. Indeed, by being more aggressive itself, the EU gets either 1 (10 out of 22) or 2 (10 out of 22). Most of the time therefore, (20 out of 22) the EU gets a good outcome.

This implies that as the US threatens to impose sanctions, the EU must effectively match the threat with actions! And this is true irrespective of whether the US actually has less to lose (in fact, the rhetoric will have us believe that this number (-1) should even be positive – not negative all all), or if it is just bluffing. It is the only way for the EU to avoid ending up in the position of having 0 all the time, as the US claims 2, and instead occasionally claiming the 2 for itself. In the process, however, free trade is in very real danger of collapsing.

This is actually why the rhetoric that is coming out of Washington is not just an act of protectionism that distorts bilateral trade; it is a threat to the world multilateral system, as it induces retaliatory aggression.

And this is why the EU has important reservations: it wants to act as a defender of the multilateral system. To this end, it is adopting an attitude of appeasement, containment and negotiation. And it is a reasonable (in the first instance, at least) reaction, to a game that effectively should never be played. But here we are, forced into an aggressive game of chicken, in which the effort to appease also amounts to admitting defeat.

So, what should be the EU’s reaction?

First, be prepared to act. Adopting measures that can impact the US economic interests in Europe need to be prepared, and in place to be used.

Second, part of the language of diplomacy should, in my view, argue what many also have argued: that trade is not a zero-sum game. Instead, we need to establish that trade is a win-win, and therefore also a lose-lose game. This should force the US to reconsider how much it loses and readjust.

Third, the EU has always seen itself as a defender of the multilateral system. While I no doubt believe that an EU-US trade war will be very distortionary for world trade given the size of the two players, there is still trade with other countries. The EU should try to protect and maintain open trade with the rest of the world and remain consistent with the role of defending free and open trade.

We might not want to sing to Trump’s tune, but we should sing to our own.

Technical appendix

In the game of ‘Chicken’ there are no dominant strategies, and although one might think that (Cooperate, Cooperate) is a likely outcome it is not a Nash equilibrium (in pure form).

Table A.1: Matrix of Pay-outs

EU

US Cooperate Sanction Cooperate 1 , 1 0 , 2 Sanction 2 , 0 -10 , -10





Note: red numbers are pay-offs for the US and blue numbers are pay-offs for the EU.



There are two pure form strategy Nash equilibria: (Cooperate, Sanction) and (Sanction, Cooperate) and none of them is the ‘good’ outcome.

US EU

S,C C,S Nash

C,S S,C Nash

The two equilibria are indistinguishable in value terms, so how is the game decided? To inform that we need to move to likely actions in order to assess likely outcomes (mixed strategies).

The mixed strategy equilibrium is determined in the following way. What does the US stand to gain if it were to Cooperate? This depends on what the EU does. We calculate that as follows:

E(V) C US =p C EU*1+p S EU*0

And what does the US stand to gain if it were to impose Sanctions?

E(V) S US=p C EU*2+p S EU*(-10).

If the US would have a higher expected value from one strategy, it would simply pursue it! The US would want to Sanction but the EU would have to Cooperate for the US to get 2. The EU in turn, would want the US to Cooperate so that it could sanction and itself get 2. But watch how the US expected values depend on the probability that the EU pursues its own strategies.

The US would want to naturally Sanction more but the EU is applying its probabilities to prevent that. The mixed strategy equilibrium is when the expected values are equal.

This implies that:

E(V) C US=E(V) S US,

and,

p C EU*1+p S EU*0= p C EU*2+p S EU*(-10).

Re-arranging this expression and remembering that (p C EU+p S EU =1) gives:

p C EU=10p S EU,

and therefore,

p C EU=10(1-p C EU) → p C EU=10/11, p S EU=1/11.

The mixed strategy equilibrium implies that EU Cooperates with a probability of 10/11 and Sanctions with a probability of 1/11. The game is symmetric in the pure form pay-offs, so that the same mixed strategy is applied by the US. In other words,

E(V) C EU =p C US*1+p S US*0

E(V) S EU=p C US*2+p S US*(-10),

which leads to p C US=10/11, p S US=1/11.

Here are the probabilities of different events happening that can be used to calculate the mixed strategy equilibrium:

Table A. 2 Probabilities

EU

US Cooperate Sanction Cooperate ( 10/11 )* ( 10/11 )=100/121 ( 10/11 )* ( 10/11 )=10/121 Sanction ( 1/11 )* ( 10/11 )=10/121 ( 1/11 )* ( 1/11 )=1/121

Notes: probabilities add up to one to exhaust all possible outcomes.

And to calculate the expected pay-offs we would need to multiply the outcomes with their respective probabilities.

Modelling current US trade policy

The game is played as follows: The US announces it will impose sanctions. And the way this is announced is that they effectively argue that they have very little to lose by doing so. This means that their loss is much smaller when the bad outcome arises (this is the only way to threaten).

The logic of this threat can be captured by reducing the losses that the US gets in the very worst outcome (i.e. less to lose: from -10 to -1). The table of pure form pay-offs can then be described as follows:

A.3 Payoffs with current US trade policy

EU

US Cooperate Sanction Cooperate 1 , 1 0 , 2 Sanction 2 , 0 -1 , -10

Note: red numbers are pay-offs for the US and blue numbers are pay-offs for the EU.

The pure strategy equilibria are the same again: (Cooperate, Sanction) and (Sanction, Cooperate).

US EU

S,C C,S Nash

C,S S,C Nash

And again, there is no welfare criterion for choosing between the two. This pushes to the mixed-strategy domain.

The mixed strategy equilibrium is determined in the following way.

E(V) C US =p C EU*1+p S EU*0

E(V) S US=p C EU*2+p S EU*(-1).

The EU needs to mix their strategies so that US’s expected value from each pure strategy is the same. This implies that:

E(V) C US=E(V) S US

or,

p C EU*1+p S EU*0=p C EU*2+p S EU*(-1)

p C EU =2p C EU-p S EU

p S EU =2p C EU-p C EU

p S EU =p C EU =1/2.

What about the US?

E(V) C EU =p C US*1+p S US*0

E(V) S EU=p C US*2+p S US*(-10),

and p C US*1+p S US*0=p C US*2+p S US*(-10),

which leads to

p C US=10/11, p S US=1/11.

The US still plays the strategies with the same probabilities! The US is still Sanctioning as rarely as it did before!!

What has changed is that the EU is pursuing the Sanctioning strategy a lot more often and as a result the world is now a very different place!

A.4 Probabilities with current US trade policy

EU

US Cooperate Sanction Cooperate ( 10/11 )* ( 1/2 )=10/22 ( 10/11 )* ( 1/2 )=10/22 Sanction ( 1/11 )* ( 1/2 )=1/22 ( 1/11 )* ( 1/2 )=1/22

Notes: probabilities add up to on to exhaust all possible outcomes.