International Trade Theory and Policy
by Steven M. Suranovic

Trade 110-1

Retaliation and Trade Wars

The analysis of tariffs in a perfectly competitive market demonstrates that when a large country imposes a relatively small tariff, or if it imposes an optimal tariff, then domestic national welfare will rise, but foreign national welfare falls. The partial equilibrium analysis shows further that national welfare losses to the exporting nation exceed the national welfare gains to the importing nation. The reason is that any tariff set by a large country also reduces world welfare.

If we assume that nations are concerned about the national welfare effects of trade policies, then the tariff analysis provides a rationale for protectionism on the part of large importing nations. However, if large importing nations set optimal tariffs on all or many of their imported goods, the effect internationally will be to reduce national welfare of its trading partners. If the trade partners are also concerned about their own national welfare, then they would likely find the optimal tariffs objectionable and would look for ways to mitigate the negative effects.

One effective way to mitigate the loss in national welfare, if the trade partners are also large countries, is to retaliate with optimal tariffs on your own imported goods. Thus if country A imports wine, cheese and wheat from country B, and A places optimal tariffs on imports of these products, then country B could retaliate by imposing optimal tariffs on its imports of say, lumber, TVs and machine tools from country A. By doing so, country B could offset its national welfare losses in one set of markets, with national welfare gains in another set.

We examine the effects of optimal tariffs and retaliation more formally by using a simple game theoretic setup. Suppose the players in the game are the governments of two large countries, the US and Japan. Suppose the US imports a set of products (A, B, C etc.) from Japan while Japan imports a different set of products (X, Y, Z, etc.) from the US. We imagine that each country's government must choose between two distinct trade policies, free trade and optimal tariffs. Each policy choice represents a game strategy. If the US chooses free trade then it imposes no tariffs on imports of goods A,B,C etc. If the US chooses optimal tariffs then it determines the optimal tariff in each import market and sets the tariff accordingly. Japan is assumed to have the same set of policy choices available.

In the adjoining diagram, US strategies are represented by the two columns, Japan's strategies correspond to the two rows. The numbers represent the payoffs to the countries, measured as the level of national welfare realized in each country in each of the four possible scenarios. For example, if the US chooses a free trade policy, while Japan chooses to impose optimal tariffs then the payoffs are shown in the

box. Japan's payoff is below the diagonal while the US payoff is above the diagonal. Thus, Japan gets 120 units of welfare while the US gets 70 units.

Note that the size of the numbers used in the example is immaterial but, how they relate to the numbers in alternate boxes is not. We will use the results from the tariff analysis section to inform us about the relationship between the numbers.

To begin, let's assume that each country receives 100 units of national welfare when both the US and Japan choose free trade. If Japan decides to impose optimal tariffs on all of its imports, and the US maintains its free trade position, then a partial equilibrium welfare analysis suggests that,

(1) Japan's welfare will rise (we'll assume from 100 to 120 units),

(2) US welfare will fall (we'll assume from 100 to 70 units), and

(3) world welfare will fall (thus the sum of the US's and Japan's welfare initially is 200 units, but falls to 120 + 70 = 190 afterwards).

Similarly if the US were to impose optimal tariffs on all of its imports while Japan maintains free trade, then the countries will realize the payoffs in the box. The US would get 120 units of welfare while Japan gets 70. To keep the example simple we are assuming that the effects of tariffs are symmetric. In other words, the effect of US optimal tariffs on the two countries is of the same magnitude as the effects of Japan's tariffs.

Finally if both countries set optimal tariffs against each other then we can simply sum up the total effects. Since each country's actions raise its own welfare by 20 units and lowers its trade partner's welfare by 30 units, when both countries impose tariffs, national welfare falls to 90 units in each country.

To determine which strategy the two governments would choose in this game, we need to identify the objectives of the players and the degree of cooperation. Initially we will assume that each government is interested in maximizing its own national welfare, and that the governments do not cooperate with each other. Afterwords we will consider the outcome when the governments do cooperate.

The Non-Cooperative Solution (Nash Equilibrium)

A non-cooperative solution is a set of strategies such that each country maximizes its own national welfare subject to the strategy chosen by the other country. Thus, in general, if the US's strategy (call it r) maximizes US welfare when Japan chooses strategy (s) and if Japan's strategy (s) maximizes Japan's welfare when the US chooses strategy (r), then the strategy set (r,s) is a non-cooperative solution to the game. A non-cooperative solution is also commonly known as a Nash Equilibrium.

How to Find a Nash Equilibrium

One can determine a Nash equilibrium in a simple two player, two strategy game by answering the following series of questions. First, choose a strategy for one of the players. Then ask,

1) Given the policy choice of the first player, what is the optimal policy of the second player?

2) Given the policy choice of the second player (from step one), what is the first player's optimal policy choice?

3) Given player one's optimal policy choice (from step two), what is the second player's optimal policy choice?

Continue this series of questions until neither player switches its strategy. Then, this set of strategies is a Nash equilibrium.

In the trade policy game the Nash equilibrium or non-cooperative solution is the set of strategies (optimal tariffs, optimal tariffs). That is, both the US and Japan would choose to implement optimal tariffs. Why?

First, suppose the US chooses the free trade strategy. Japan's optimal policy, given the US choice, is to implement optimal tariffs. This is because 120 units of national welfare is greater than 100 units (see diagram). Second, if Japan chooses optimal tariffs, then the US's optimal policy is optimal tariffs, since 90 units of welfare is greater than 70 units. Finally if the US chooses optimal tariffs, then Japan's best choice is optimal tariffs since 90 is greater than 70.

The Cooperative Solution

A cooperative solution to a game is a set of strategies which would maximize the sum total of the benefits accruing to the players. In some instances a cooperative outcome may require the transfer of goods or money between players to assure that each player is made better-off than under alternative strategy choices. In this game, such a transfer is not required, however.

The cooperative solution in the trade policy game is the set of strategies (free trade, free trade). At this outcome, total world welfare is at a maximum of 200 units.

Implications and Interpretations

First of all, notice that in the non-cooperative game, each country is acting in its own best interests and yet the outcome is one that is clearly inferior for both countries relative to the cooperative strategy set (free trade, free trade). When both countries set optimal tariffs, each country realizes 90 units of welfare while if both countries pursued free trade, each country would realizes 100 units of welfare. This kind of result is often referred to as a prisoner's dilemma outcome.(1) The dilemma being that pursuit of self-interest leads to an inferior outcome for both participants.

However, without cooperation it may be difficult for the two countries to realize the superior free trade outcome. If both countries begin in free trade, each country has an individual incentive to deviate and implement optimal tariffs. And if either country does deviate, then the other would either suffer the welfare losses caused by the other's countries restrictions or would retaliate with tariff increases of one's own in order to recoup some of the losses. This scenario in which one country retaliates in response to another's trade policy could be thought of as a trade war.

This story closely corresponds with events after the Smoot-Hawley tariff Act was passed in the US in 1930. The Smoot-Hawley tariff Act raised tariffs to an average rate of 60% on many products imported into the US. Although it is unlikely that the US government set optimal tariffs, the tariffs nevertheless reduced foreign exports to the US and injured foreign firms. In response to the US tariffs approximately 60 foreign nations retaliated and raised their tariffs on imports from the US. The net effect was a substantial reduction in world trade which very likely contributed to the length and severity of the Great Depression.

After World War II, the US and other Allied nations believed that high restrictions on trade were detrimental to growth in the world economy. The General Agreement on Tariffs and Trade (GATT) was initiated to promote trade liberalization among its member countries. The method of GATT was to hold multilateral tariff reduction "rounds". At each round countries would agree to lower tariffs on imports by a certain average percentage in exchange for a reduction in tariffs by other countries by an equal percentage. Although GATT agreements never achieved a movement to free trade by all member countries, they do represent movements in that direction.

In a sense then, the GATT represents an international cooperative agreement which facilitates movement towards the free trade strategy set for all countries. If a GATT member nation refuses to reduce its tariffs, then other members would refuse to lower theirs. If a GATT member raises its tariffs on some product above the level that it had previously agreed, then the other member nations are allowed, under the agreement, to retaliate with increases in their own tariffs. In this way nations have a greater incentive to move in the direction of free trade and a disincentive to take advantage of others by unilaterally raising their tariffs.

The simple prisoner's dilemma trade policy game then, offers a simple explanation of the need for international organizations like the GATT or the WTO. These agreements may represent methods to achieve cooperative solutions between trading countries.


1. The prisoner's dilemma name arises from an early version of this type of game in which the two players are prisoners who have committed a crime together. Go Back.

International Trade Theory and Policy - Chapter 110-1: Last Updated on 3/3/01

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