Question

23. Game theory of Trade War. Two Players: China and the United States: Two choices: Raise tariff by 25% or leave tariffs alone. If both countries raise tariffs, each country’s GDP decreases by $200 billion. If neither country raises tariffs, each country’s GDP remains the same. If only one country raise its tariff, its GDP increases by $600 million and the other country’s GDP decreases by $400 billion. Draw the payoff matrix and find the Nash equilibrium.

Answer 1

The matrix is drawn below

		China
		Raise tariff	Leave tariff
United States	Raise tariff	(-200, -200)	(600, -400)
	Leave tariff	(-400, 600)	(0, 0)

We investigate the matrix and find that

• For US, when China raises tariff, its best response is to raise tariff and have a lower GDP loss at 200 billion. When China leaves tariff alone, its best response again is to raise tariff and have a higher GDP increase at 200 billion. Hence raising tariff is a dominant strategy
• The game is symmetric so China also has a dominant strategy of raising tariff
• Hence, the NE is (-200, -200) when both countries raise tariff.