US-China Trade war: A game theory

by Throwaway1546320


US-China have been moving towards a “war” scenario for quite some time. There are two great ways to model this. The first being the Thucydedes Trap. The story is a small one. But as China challenges America’s predominance, misunderstandings about each other’s actions and intentions could lead them into a deadly trap first identified by the ancient Greek historian Thucydides. As he explained, “It was the rise of Athens and the fear that this instilled in Sparta that made war inevitable.” The past 500 years have seen 16 cases in which a rising power threatened to displace a ruling one. Twelve of these ended in war.

Of the cases in which war was averted — Spain outstripping Portugal in the late 15th century, the United States overtaking the United Kingdom at the turn of the 20th century, and Germany’s rise in Europe since 1990 — the ascent of the Soviet Union is uniquely instructive today. Despite moments when a violent clash seemed certain, a surge of strategic imagination helped both sides develop ways to compete without a catastrophic conflict. In the end, the Soviet Union imploded, and the Cold War ended with a whimper rather than a bang.

The second model for the US-China trade war is war of attrition. Attrition warfare is a military strategy consisting of belligerent attempts to win a war by wearing down the enemy to the point of collapse through continuous losses in personnel and material. The war will usually be won by the side with greater such resources. The word attrition comes from the Latin root atterere to rub against, similar to the “grinding down” of the opponent’s forces in attrition warfare. In the first world war France and Germany fought in the trenches and lost 250K people and barely moved an inch. Economists have used war of attrition to explain why governments often wait too long before implementing the right policies.

This is the most ideal way in my opinion to model the current trade war with a game theory version of war of attrition.

The basic rules of the game are simple:

Two players are fighting over a prize At any time, a player can concede, allowing the other player to claim the prize There is a cost to each player for playing the game The 1st Equilibrium of this game :The Game is over before it even begins

The logic is straightforward: Given there is a cost to playing the game, if a player believes he is going to concede eventually, he might as well concede as soon as possible.

The 2nd Equilibrium: A long and debilitating fight

Few assumptions:

Prize is worth Z to each player Cost of playing the game for each player is C The probability of a plyer fighting in any period is P Two Strategies for the Player:

Strategy 1:

If he decides to fight in Period 1, his payoff is -C with a probability P and Z with probability 1-P. In other words his expected payoff is just -PC + (1-P)Z.

Strategy 2: If a player decides to concede in period 1, then his payoff is zero.

Nash Equilibrium:

A player is indifferent to the strategies available to him

Setting these two payoffs equal to each other we have : -PC + (1-P)*Z = 0

Cost of brinksmanship can last longer than what is in everyone’s interest.

The probability of a player choosing to fight goes up when the value of the prize goes up. The number of periods the game has already been played has no bearing on the probability of a player choosing to concede or fight in any given period. The probability of a long drawn-out fight can be very high. Assuming Z = 10 an C = 1 (i.e the reward is only 10 times greater than the cost of fighting in each period) P=90%. IF Z = 5 and C=1 then P = 83%. This means that even if the prize was cut in half, the probability only drops from 90% to 83%. So what is at stake here: What is the final prize to the players?

Estimates have shown that IP theft from CHINA is around 500 Billion US Dollars a year. Do you know how many walls can be built with that? How many social programs can be done in USA with even half the money?

We can have education, healthcare and a higher minimum wage for all Americans and provide for refugees coming into the country if we brought back even half of that.

What is holding back Trump?

Trump is in a great spot right now with highest approval rating in a while, an economy and stock market firing on all cylinders (assuming fed cuts but that is a for a different post), unemployment at its lowest and we are adding 160K new jobs in America (NFP). He can wait until election time to get or force a deal. The impact to USA from tariffs is much lower than China. Some estimates say 0.1% to US GDP compared to 0.4% to China (maybe higher).

Trump does have a large issue at home where he is fighting a battle with the democrats. This does not help his situation as he is up for re-election whereas President Xi is not. The rhetoric at home further complicate the effort to find a compromise.

China is trying to assert their dominance as a world super power and has promised its people that they will be a powerhouse by 2049. There is a massive belt and roadway initiative going on with Chinese government and several countries around the world. If China goes further into recession they will have to defend their economy by adding further stimulus which would mean taking money away from other initiatives. The people of china have been tolerant of all the rules of this authoratian government on the back of the fact that quality of living and income has gone up significantly in the boom in China in the last several years. If the country falls into a deep recession, there could be further revolts. The hawkish side of the ruling party in China does not want to show any weakness to USA.

There is clearly a lot at stake here which increases the final prize Z resulting in a potentially long drawn out battle.

Side note: US yields will be pushed a lot further down in reaction to China devaluating their currency aggressively. Lots of uncertainty from these moves will result in a extreme dovish fed. Long Eurodollar December 2020 trade is my play.

The question is who makes the concession…who folds?