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Are we on the brink of a global trade war? Tariffs imposed by the US on imports of steel and aluminium from the European Union, Canada and Mexico, and the retaliation they are about to take have raised such fears. Over the weekend, finance ministers of the world’s leading economies met in Canada ahead of a G7 summit to voice concern.

The backdrop is one of rising protectionist measures since the financial crisis a decade ago, but the US now seems to be taking the game to another level. The current situation is reminiscent of the 1930 Smoot-Hawley Tariff Act, meant to boost a crisis-hit US economy by protecting American jobs and farmers.

However, the ensuing trade war affected thousands of products and resulted in average tariffs in the US of 50 per cent, meaning that goods sold at $1 on international markets ended up costing $1.50, which harmed economies. Many analysts agree that this deepened the Great Depression and contributed to events leading to the second world war. Some fear history may repeat itself.

Game theory – which uses maths to study strategic interaction – can help evaluate the likelihood of a full-blown trade war this time. Free trade is commonly viewed by economists as more efficient than protectionism, creating more wealth for participants. Game theory commonly conceptualises trade relations as a prisoner’s dilemma game, in which cooperation between two prisoners (refusal to betray one another) brings the greater gain (minimum jail time) than mutual betrayal.

When countries trade so extensively, as they do today, free trade can be sustained with “tit-for-tat” strategies: if a country unilaterally raises trade barriers, its partners enter a trade war that creates the prospect of sufficient long-term losses for both sides that the original transgressor is brought back to respecting the free trade agreement. Protectionism is only beneficial for a nation if its trading partners are expected not to retaliate.

Not-so-free trade

To explain why the US seems to be moving away from free trade, several other factors ought to be considered. First, the US economy is in good shape, with its , the lowest since April 2000. This gives its trade negotiators more leeway, since countermeasures that might cause job losses and create inflation will appear less frightening.

Second, US tariffs on steel and aluminium show that president Donald Trump has been responding to the demands of his supporters as mid-term elections near, setting the scene for a second mandate. Eager to protect his base, Trump will probably nullify the effect of retaliatory tariffs targeting US products such as whiskey or motorcycles with targeted support such as subsidies to affected industries.

It is also worth noting analyses that say the cost of similar US trade skirmishes with China , thus producing big political gains for Trump at a small electoral cost.

None of the countries recently targeted by the US steel and aluminium tariffs has a similarly comfortable bargaining position. They are all highly dependent on commercial ties with the US, and in the EU’s case, its lack of structural cohesiveness is spiced up by recent political instability such as Brexit. As such, the only credible retaliatory threats these trading partners can wield will be small and measured, which lessens the prospects of escalation to a full “trade war”.

Bringing China into the picture adds further rationality to Trump’s stance. Due to its $350 billion trade deficit with China, the US has threatened to impose tariffs on $50 billion of Chinese imports. Trump’s message to China from the tariffs that hit Canada, Mexico and the EU is clear: if that is how I treat my allies, imagine the fate of my enemies.

By credibly communicating the capacity to bear retaliatory costs, the US has just improved its bargaining power. This negotiating chip is likely to be used to gain concessions, rather than as the opening move in an all-out trade war.

Read more: How humans are born to trade; Game theory says you should charge your friends to borrow things