To Play or Not to Play: A Game Theoretic Analysis of Trade War

Illustration by Allen B Thangkhiew

In May this year, as the world dealt with the spectrum of horror that the pandemic brought with it, we also witnessed the slow degeneration of the China-Australian trade relationship.

China has historically been Australia’s number one export market, accounting for about 25% of total Australian exports. Then Covid-19 happened and the world changed.

China, on May 19th placed a tariff of a whopping 80.5% on Australian barley, only days after having banned beef exports from four Australian exporters. The China-Australia trade relations seem to be whirling in a downward spiral, ostensibly because of Australia’s call for an international inquiry into the origins of the COVID-19 pandemic.

For us to really understand what it means, for China to act aggressively in trade scenarios, it is important to understand the Sino-American Trade war, that started in January 2018, with Trump’s approval of global safeguard tariffs on $8.5 billion in imports of solar panels and $1.8 billion on washing machines. This was followed by a series of retaliations, by China and USA to eventually boil down to a situation now termed as a ‘Trade War’. The gist of which is- President Trump levied tariffs on Chinese goods, to which Xi Jinping responded with his own new set of tariffs, to which Trump added more tariffs and so on.

An interesting way of theorising this tit-for-tat is with game theory, using which, we can find the optimal outcome from a set of different choices, analysing the valuation and the associated costs of two parties battling each other. The evolutionary game theoretic strategies that are presented to us in the Hawk and Dove game framework explain the inevitability of conflict when faced with the possibility of aggressive retaliation in tariffs. Equilibrium in the Prisoners Dilemma game framework, on the other hand, emphasises the impossibility of cooperation in such a situation, characterised by an absolute lack of trust between the two countries. Both these games are of conflicting interest, and highlight different aspects of the ongoing Sino-American trade war.

Hawk and Dove game:

The Hawk and Dove game, was first formulated by John Maynard Smith and Georg Price in ‘The logic of animal conflict’ and has since become an integral part of basic game theory lectures. The concept is simple- a hawk is aggressive and confrontational in nature, and a dove avoids conflict. So, consider Hawk and Dove to be two strategies that both China and USA can play individually. Starting from a point of President Trump levying tariffs on a Chinese product, what would China’s best response be? Consider the matrix:

 

Here, V represents the value that the country may place in retaliation, whereas C represents the cost of retaliation.

So, here’s the deal- to win you must act aggressively, and the one that acts non-aggressively is the loser. The ideal scenario here is to act aggressively, while the other party acts ‘non-aggressively’. The catch, however, is if both countries act aggressively (thinking about their own gain, of course), that is, if the trade war continues, it injures both economies, and both lose. Bertrand Russel compared Nuclear Brinkmanship to a similar game. If we think about a situation in which both countries play non-aggressively, then both don’t lose anything, but in that, there is always the temptation of an aggressive policy which will make you win as opposed to just not losing.

Now, to look at the Prisoner’s Dilemma framework;

Prisoners Dilemma:

This game, originally framed by Merrill Flood and Melvin Dresher is a game of cooperation. In Prisoners Dilemma, two players are isolated, which means they act individually, and they can either cooperate with each other, or defect altogether, such that, they reach their highest pay-off. When we talk about the China-USA trade war scenario, trust between the two countries is already eroded, there is no reason for them to communicate and reveal their strategy, and if both defect, they are both injured. Consider the matrix:

Here, the two players are the two countries that we are considering- China and the USA. The two strategies that could be played are to Impose Tariff (T), or to continue with Free Trade (F). The greatest payoff that both countries could receive, that is, their greatest benefit lies in playing (F,F)- that shows, there is highest payoff in a situation of cooperation between the two. But a greater payoff that a country could obtain by imposing tariffs, while the other does not, does seem enticing. Which explains why countries tend to defect rather than cooperate. When this game is played again and again, it is seen that cooperating, while the other defects is a losing strategy- which explains tariff retaliation, and also explains why countries could end up in the situation of a trade war.

When we look at the same game framework as what is called an extensive game (shown above), it’s easy to see that whether the USA plays T, or F, it is in China’s best interest to play T- in order to receive a greater payoff. Prisoners dilemma tells us, that a Trade War is the general state- it provides stability to the game.

In the Australian context however, let’s think of it in the form of a Hawk and Dove game, we know that it is impossible to avoid conflict, and we know that two can play a game, but after understanding it collateral damage; Perhaps, it is better that neither play this one.

Author: Urvi Dhar

Urvi is a Masters student of Economics at the Gokhale Institute of Politics and Economics, Pune. She pursued her undergraduate degree in Mathematics from Ramjas College, University of Delhi, and is always striving to harmonise the two in her research. With an intrigue for policy driven research, her deepest interests lie at the intersection of International and Development Economics.
When she isn’t reading, you’d find her fiercely engrossed with board games and puzzles!

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