Then we are out of any rationality, ending with both parties losing. In that case I'd guess that a player trying to win against every single other at the same time will be the ultimate loser.
from the point of maximising value in the economy its a game where in a single iteration co-operate is strictly better than any alternative. if the other player co-operates then that is the best outcome. if the other player defects then you are still better off co-operating than defecting.
but the problem is the real game being played is different because the political process ends up diverging from maximising value in the economy. the free trade argument is this is because the political process is captured by concentrated interests who benefit from tariffs to reduce competition. the deadweight loss caused by tariffs to the rest of society is not properly accounted for in the political process because the cost is diffused over many people. other people who accept the text book comparative advantage argument but reject free trade will claim to have a different optimisation function that is not purely maximising value in the economy. for example maybe they think its important to have a strong manufacturing base in order to make it easier to re-arm to fight a conflict.
but if we accept this situation then its difficult to say what the optimal strategy is because you don't really know the payoff matrices for the players. even what they tell you could be a lie and might be difficult to derive what their values are based on their actions.
Make things painful enough that one of the players decides to change their strategy (e.g, by changing who has been delegated decision-making authority. Hopefully.)
You also have to consider the longevity of your strategy. Trump might not care about the value function, but over the longer term the EU could make a bet that the US does and will, one way or another, return to leadership that does. And indeed, they seem to craft tariffs to cause that to happen faster.
