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Does Trump play Nash?

On the 20th January of 2017, it was the inauguration day of the 45th president of the United States: Donald John Trump. Many economists argued that the election of the American businessman would lead to geopolitical time bombs between the U.S. and other large open economies. One of the main objectives of the Trump administration is the implementation of a protectionistic U.S. economy. A large wall along the border of Mexico, open threats of trashing German car companies with import tariffs of 35 percent, and the accusation of China that they are manipulating the dollar exchange rate of their domestic currency: the Renminbi. ‘We Will Make America Great Again’, right?

The main question that will be answered in this article is: where does the latter accusation come from? First, everyone who is reading this article should reach for a piece of clothing in their closet and look at the clothing label. Does the label say: ‘Made in China’? There is a high chance that this will be the case. According to the World Bank, China has the largest export economy in the world with an export level of over $2.2 trillion. If we normalize the export levels of China as a percentage of GDP and compare it with the United States (22,1 vs 12,6), we can come to the conclusion that China is more of a ‘trading nation’ than the U.S. This is mainly driven by the sale of goods and services in industries that are related to electronics (think about that Huawei phone or Lenovo laptop you just bought this year). Additionally, the United States has a trade deficit with China which means the U.S. imports of goods and services from China are higher than the level of exports to China.

Consequently, China sells a lot of goods and services to U.S. firms and consumers. Chinese exporters in return receive dollars but can’t do anything with this foreign currency. Managers of Chinese firms have to pay their employees’ wages, buy raw goods to manufacture and remain a profit to pay out as a dividend to shareholders all in their local currency the Renminbi. Demand for Renminbi and the Supply of Dollars increases when Chinese exporters sell goods to the U.S. This will lead to a depreciation of the Dollar and an appreciation of the Renminbi.

Indeed,  one of the main concerns for a trade-dependent country like China is battling exchange-rate risk. This kind of risk occurs when the value of an investment will increase or decrease due to a change in the exchange rate of 2 currencies. In our case, the value of Chinese goods will be more expensive for the U.S. when the value of the USD depreciates against the CNY (Chinese Yuan Renminbi). If for example the exchange rate USD/CNY is 2/1 this means that for every CNY American importers have to ‘give up’ 2 USD. If this ratio changes to 3/1, because for example an increase in both the supply of dollars and demand for Renminbi, this will be disadvantageous for both China and the U.S. For the American consumers because they have to exchange more USD for CNY, and thus effectively Chinese products become more expensive for them. Appreciation of the Renminbi against the Dollar will, in this case, lead to costlier Chinese exports and higher unemployment in China due to losing export business. China will subsequently risk its position as a trading nation if it doesn’t find a way to actively intervene in the Foreign Exchange Market.

As a result, China has an incentive to ‘manipulate’ the USD/CNY exchange rate. In order for China to maintain their export-led growth, they have to reverse the effect of the appreciation of the Renminbi against the dollar. The Central Bank of China (People’s Bank of China) has various policy instruments to achieve the goals of their chosen monetary policy.  An example of active intervention that is used by the PBOC is a non-sterilized intervention. The Central Bank of China has the power that it can print Renminbi without any limitations. The PBOC buys excess U.S. dollars from Chinese exporters and give them the newly printed Renminbi. This will lead to scarcity of U.S dollars, increases the supply of Renminbi which eventually will lead to a depreciation of the Renminbi and decreases the USD/CNY exchange rate. This is done until it will return to a (fixed) exchange rate of 2/1 before the non-sterilized intervention of the PBOC. The PBOC now has pilling amounts of U.S. Dollars in its foreign exchange reserves, seeking to make a return on these reserves the PBOC looks for a dollar denominated low risk security to invest in: U.S. Government Bonds.

Like loyalty, the purchase of US treasury bills by China is a two-way street. PBOC buys billions of dollars’ worth of US debt as a riskless investment with the excess dollars bought from Chinese exporters. With the purchase of U.S. debt China essentially lends money to the U.S. so they can keep buying Chinese products. On the other hand, by accumulating U.S. debt, China drives the price of Treasury Bills up, and is consequently keeping U.S. interest rates low, which is part of the expansive fiscal policy of Trump.

With this in mind, we can use a subset of Industrial Organization to analyse the strategic interaction between 2 or more economic agents: Game Theory. In Game theory, the goal of every economic agent is to choose its best response given the response of the other party. In our case, we have a two stage dynamic game where the two economic agents are Donald Trump and the PBOC. We assume all economic actors are rational by choosing the strategy which maximizes their profits.

The agents interact in the following way: Trump firstly picks its foreign policy by choosing between a protectionistic or a free trade approach. A free trade approach consists of keeping everything the way it is: the U.S. still keeps issuing government bonds to finance its federal deficit and takes for granted the fact that a lot of American firms outsource jobs to China because of low wages (profit of U.S and China are 70 vs 100). In a protectionistic approach, Trump will send a lot of negative tweets which says the U.S. wants to decrease its trade deficit and puts pressure on China to stop buying excess dollars from Chinese exporters.

Subsequently, the PBOC observes the foreign policy of Trump and decides which action it will take. After the protectionistic approach, The PBOC can either choose for the offensive strategy ‘fire sale’ where it will sell all of its accumulated U.S. debt which will decrease the price of treasury bills and increase the U.S. interest rate. This will also affect China because it will lose one of its main trading partners by throwing it into a deep recession (profits for both countries are 0). On the other hand, it could choose to follow a defensive strategy. China will keep accumulating U.S. debt and chooses to keep the same exchange rate regime initiated by the PBOC. This will cool off the relationship between the 2 countries, lead to more uncertainty and has a negative effect on trade (profits for both China and America will decrease to 50).

We can solve this dynamic game by the means of backward induction to find the subgame perfect Nash equilibrium. We first look at the final stage where China will choose a strategy, knowing Trump chose a protectionistic approach. It can choose between an offensive strategy or a defensive strategy. In this subgame, China will choose a defensive strategy because its profits are higher than if they would choose an offensive strategy (50 vs 0). After solving the first subgame we turn to the second subgame. The choice of Trump between a protectionistic and a free trade economy, knowing China will choose a defensive strategy if Trump chooses a protectionistic strategy. Trump should be a rational economic agent and choose to follow a free trade strategy (70 vs 50 profit). So in the subgame perfect Nash equilibrium, the U.S. chooses a free trade policy, and China chooses a defensive strategy (profits for China and U.S. respectively are 100 vs 70).

However, there is a downside of using Game Theory in analysing strategic interaction in the U.S. government bond market. One of the main disadvantages goes back to a basic assumption used in economic theory: the assumption that economic agents are rational and choose the strategy that maximizes their utility. Is Trump really an individual who can be seen as rational, or will he choose a strategy that will throw both China and the U.S. in a deep recession just to keep his credibility towards his loyal voters?


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