“In terms of economic growth, no one wins in a trade war. In terms of geopolitical rivalry, what matters is who lose more.” Bloomberg chief economist Tom Orlik Said.

And this will be the basis of the payoff structure that I will use to analyse the trade war between the US and China. All payoffs will be negative, indicating the economic cost of engaging in the war.

Payoff Structure

The payoffs here are based on the potential effects on each country’s economy, including the risks of diminished growth and increasing uncertainty. At the first node, stopping will give a negative payoff to both countries (for simplicity, this is equal for both countries). At the third node, abandoning the course will give a more costly, negative payoff as the trade war progresses. China’s compliance signals a victory for the US and a corresponding defeat for China. Here, we assume that u < 10.

Yet, a more complicated and difficult-to-model structure will arise if we consider the individual payoffs to these politicians. Trump’s own economic metrics and his chances at re-election contribute to his payoff while Xi’s payoff probably has a more direct linkage to the well-being of the economy.

Solution to the game

Unfortunately, by “solution”, I do not refer to a panacea to the trade war but rather, the theoretical outcome predicted by game theory. Here, we assume that all players are rational and there is common knowledge of rationality (obviously, this is false).

Solving the game by backwards induction, we observe that at the third node of the game tree, Trump has to decide if he wants to continue the trade war or abandon his protectionist course. If Xi believes Trump to be rational, Xi will conclude that Trump will abandon course because the payoff to China of –u is infinitely greater than -∞.

Therefore, at the second node, Xi will retaliate, because this will give China a higher payoff of -10 compared to – u that will result from complying with the tariff hike.

Ultimately, at the first node, a rational Trump would have stopped engaging in the trade war. This would be the sub-game perfect equilibrium of the game.

However, this hinges on common knowledge of rationality and that both players are rational.

Adding a layer of complexity to this game, we can factor in Trump’s irrationality (which might well be a tactic of his). Xi’s belief of Trump’s irrationality translates into Xi believing the possibility of Trump choosing to stay the course at the third node. This is a “credible threat” because of Trump’s legal powers and the signals he has been sending reveals his willingness to expand the trade war. Trump’s staying the course will give China a payoff of -∞. Hence, at the second node, Xi will choose to comply.

Where we are now

On May 10, US President Donald Trump ordered a tariff hike on US$300 billion worth of remaining imports from China, which puts global growth at risk and generates uncertainty in financial markets. Beijing reflexively responded by vowing to take the necessary countermeasures. Since last year, the standoff has weighed heavily on both countries’ manufacturing sectors.

So, what is the point of this analysis?

If there is anything this simple model can educate us on, it is that irrationality is an important tactic. Trump’s larger-than-life presence, his eccentric tweets, and inconsistent behaviour (he slammed another tariff hike two days after tweeting that the Washington trade talks were “candid and constructive”), are signals of his irrationality and unpredictability. Traditional cost-benefit analysis is blurred in the trade war, and China must react strategically.

Cover photo from https://edition.cnn.com/2019/05/23/economy/trade-war-economy/index.html