MENU

Globalization in a Game Theory Perspective

The greater Cleveland area is consistently ranked as one of the of the cities hardest hit by globalization. The manufacturing industry, once the majority of the economy of Cleveland, has been steadily declining due to competition with other countries with cheaper labor. According to my grandma, most people in her high school didn’t even bother with college, they just got a job at the local factory. Even in many high schools today in Akron and Cleveland, many students are unable to go to college, so they rely on jobs like manufacturing that don’t require a degree. With the steady decline in American manufacturing, there are fewer and fewer opportunities for this population. This contributes to economic inequality and the US’s current political climate.

 

Many manufacturing jobs are at risk for automation or relocation to countries with cheaper labor markets. While these jobs are lost, however, manufactured goods become cheaper, which is a positive for many Americans. Also, as companies cut manufacturing costs, they are able to expand faster, and end up creating more jobs than are lost, according to a report cited by the Economist. For example, a bank saves money by using ATMs, rather than paying in-person tellers, and thus open more branches and hire more bank managers and investment advisors. These newly created jobs, however, tend to require more education (a teller doesn’t have the necessary qualifications to be a bank manager). There is a clear trade-off: cheaper goods and more (but more challenging) jobs, or more jobs that don’t require a college degree. I am using game theory to calculate the best policy solution to globalization, whether that be punitive tariffs (like what Trump is trying to introduce), different free trade laws, subsidization of specific industries (like the coal industry or renewable energy industry), etc..

 

Scenario: Leaders from the United States are sitting down to discuss trade policy. The United States is upset that China is producing so much steel- which keeps steel prices low, making it harder for American firms to produce their own steel. The US’s is advocating for the best interests of steel plants based in middle America. Their goal is to protect domestic steel production. They can do this by threatening to increase tariffs (or otherwise increase free trade barriers) on steel unless Chinese firms limit their production, maintaining current trade policy but support domestic steel production through infrastructure investment/subsidization/worker’s aid programs/ or tax code advantages, or they could do nothing. China can respond by also increasing barriers to free trade (starting a trade war by increasing tariffs on goods they import from the US, etc..), limiting their own steel production, or keeping the status quo. I will model this game in two slightly different ways. The first will be through a two by two matrix and find the Nash equilibrium and Pareto optimality.  This method assumes that each player is choosing their strategy at the same time and doesn’t know the other players’ strategy beforehand. In the context of this game, it means that the US and China must determine their strategy at the same time and cannot change their strategy after they have chosen one. The second way I will model this game will involve looking at this scenario as a sequential game. I will model this game through a game tree, which will show the US first choosing a strategy, and then China responding to that strategy. The second method may be more realistic, since in the real world it is unlikely that the two countries will change their policies at the same time.

 

Method One

 

Two by Two Matrix (without values)

 

China

US Strategy A B C
A (a, b) (c, d) (e, f)
B (g, h) (i, j) (k, l)
C (m, n) (o, p) (q, r)  

 

Strategies:

 

US A: threaten to increase tariffs (or otherwise increase free trade barriers) on steel unless Chinese firms limit their production (if China limits, then the tariff wouldn’t happen, but China doesn’t, then the tariff would be put in place)

 

US B: maintain current trade policy but support domestic steel production through infrastructure investment/subsidization/worker’s aid programs/ or tax code advantages

 

US C: Do nothing

 

CHINA A: increase barriers to free trade (increasing tariffs on goods they import from the US such as soybeans, semiconductors, etc..)

 

CHINA B: limiting their own steel production

 

CHINA C: do nothing

 

Values:

 

(a, b)= (-10, -10) worst possible situation for both parties because a trade war has begun. Steel prices rise in the US, helping the steel industry, but other manufacturing and farming sectors are hurt because their foreign markets are limited (due to tariffs) and they cannot expand as rapidly since the materials they need in order to grow (like steel) are more expensive. China experiences a similar effect.

 

(c, d)= (8, -5) This is the best situation for the United States because the steel market is protected and a trade war is averted. The American steel industry becomes stronger, and other parts of the economy, like agriculture, are only slightly hurt (due to slightly higher steel prices). This provides many jobs for manufacturing workers, reducing inequality, The Chinese steel firms, however, are less profitable since they cannot operate at total capacity, which hurts their economy, and looks weak since they are appeasing their opponent.

 

(e, f)= (2, -1) Although a trade war is not triggered, tariffs are still implemented, which provides some boost to the American steel industry, but slightly raises the price of steel, slightly hurting other parts of the economy. China appears strong, but loses market share of the global steel market.

 

(g, h)= (-7, 3) The broader US economy is hurt by the tariffs, but the steel industry is helped by the government. China’s economy is helped because the tariffs protect their industry, but these tariffs also lead to slightly higher prices for Chinese consumers.

 

(i, j)= (9, -4) The American steel industry is helped by government support and less competition from Chinese firms. The broader economy is only slightly hurt by slightly higher steel prices. Chinese firms are significantly less profitable since they cannot operate at full capacity.

 

(k, l)= (7, 0) The American steel industry is helped by government support, and the broader economy is not affected. Chinese firms are faced with more competition from American firms.  

 

(m, n)= (-8, -3) The broader US economy is hurt by the tariffs, and the steel industry isn’t helped at all. The Chinese economy is hurt by the tariffs due to higher consumer prices and limited access to necessary goods.

 

(o, p)= (5, -4) The steel industry is helped due to less competition from China, and the broader American economy remains unaffected. Chinese steel firms are less profitable since they are not operating at full capacity

 

(q, r)= (-1, 1) The status quo, where Chinese steel firms are more competitive than American steel firms, is unchanged)

 

Two by Two matrix  (with values)

 

China

US Strategy A B C
A (-10, -10) (8, -5) (2, -1)
B (-7, 3) (9, -4) (7, 0)
C (-8, -3) (5, -4) (-1, 1)

 

Nash Equilibrium:

 

China

US Strategy A B C
A (-10, -10) (8, -5) (2, -1)
B (-7, 3) (9, -4) (7, 0)
C (-8, -3) (5, -4) (-1, 1)

 

Nash Equilibrium solution: US: B, China A, Value (-7, 3)- The United States should play strategy B and China should respond with Strategy A. The way I found this is by eliminating dominated strategies. As shown on the table above, every single payoff for the United States in strategy B is bigger than strategy A and strategy C. If China plays strategy A, US strategy B will give the US the highest payoff. If China plays strategy B, US strategy B will give the US the highest payoff. And if China plays strategy C, US strategy B will also give the US the highest payoff. No matter what strategy China pursues, strategy B offers the US the highest payoff, so the US should always play strategy B. We use the same technique in determining China’s best strategy. Finding the Nash equilibrium assumes that each player is playing in their own self-interest and does not care about the outcome of the other player.

 

Pareto Optimality:

Pareto Optimality solution: US B, China C (7, 0) and US B, China B (9, -4)


The way the Pareto Optimal solution is found is by plotting all of the payoffs an xy graph (with the payoffs for China on the y axis and payoffs for US on the x axis). The points that are farthest to the right (highest payoffs for the US) and farthest up (highest payoffs for China) are the solution, since they represent the best mutual outcomes for the players.

 

Discussion of Two by Two Matrix:

 

The Nash Equilibrium solution is different than the Pareto Optimal solution, which makes finding the best solution difficult. The Nash solution represents how each player should play assuming that each player wants its best interest and doesn’t care what the payoffs for the other player are. In the Nash Equilibrium, the Players do not trust each other and are only looking out for themselves. The Pareto Optimal solution, however, represents the best mutual solution and allows for the players to cooperate with each other in order to gain the best mutual payoffs. For example, the payoff for the Nash Equilibrium solution is (-7, 3), and the Pareto Optimal Solutions are (7, 0) and (9, -4). Comparing the first Pareto Outcome to the Nash Equilibrium, if China were willing to give up only 3 points, the US would gain 14 points. Looking at the second Pareto Outcome, if China were willing to give up 7 points, the US would gain 16 points. In both Pareto outcomes compared to the Nash Equilibrium, the US would gain more points than China would lose- which is why the Pareto Optimal solutions represent the best mutual outcomes. However, these Pareto Outcomes are only possible if China were willing to slightly sacrifice for the greater good, which China may not be willing to do.

 

All solutions involve the US playing strategy B, the US should support the steel industry in ways that maintain current trade policy. However, they should expect China to retaliate with tariffs. Unfortunately, this strategy still results in a -7 payoff for the US. However, considering the strategies China may pursue, this is still the best option since it makes the best of a bad situation. Ohio steel workers should vote for politicians that still value free trade, but are willing to support the steel industry in ways that don’t change the status quo of trade policy.

 

Method Two

 

Sequential Game in a Game Tree:

http://goaconference.org/wp-content/uploads/2018/04/2-2-300x86.png

 

In this scenario, the game is sequential, with the US choosing the first strategy and China responding to this strategy. The payoffs are the same as in the two by two matrix since, in the end, the same policies are put into place and the only thing that changes is the timing of when the US and China choose their policies.

 

When China chooses how it will respond to US strategy, it knows each of the payoffs and will choose its strategy that gives China the best payoff. Knowing this, we can eliminate choices (starting at the bottom) that result in a worse payoff. Our new game tree looks like:

As we can see, the strategies and the payoffs still remaining represent the payoffs the US can expect from its choice. If it chooses strategy A, it can expect China to Choose strategy C (since that will result in the highest payoff for China). If the US chooses strategy B, it can expect China to choose A; and if the US chooses strategy C, it can expect China to choose strategy C. Knowing what strategies China will choose, the US can choose its strategy with the highest payoff for the US. As shown in the diagram this is strategy A. If it chooses strategy A (threaten tariffs), China will choose strategy C (do nothing), and this will result in a payoff of (2, -1).

 

Discussion of Results:

 

The payoff and strategies are completely different depending on when the US and China choose their policies, which demonstrates the value of timing your action and knowing what your opponent will do in a game. If the US acts first, it will threaten tariffs and China will not respond, which will result in a payoff of (2, -1). If the two players act at the same time, then they will not be able to predict their opponents’ action as well, leaving more options open and leaving open questions of trust. If they choose at the same time, the US will support the US steel industry and China will impose retaliatory tariffs, resulting in a payoff of (-7, 0).

 

Since it is more likely that the two players will choose their policies sequentially, the game tree scenario is more accurate, so the US should impose tariffs and China shouldn’t respond. This is actually somewhat happening right now. The US has imposed around $50 billion worth of tariffs on 1,300 Chinese goods, while China has only imposed around $3 billion worth of tariffs on 128 goods. Although imposing $3 Billion of tariffs isn’t doing nothing, it is not retaliating against the  US at nearly the same degree the US is threatening China.

 

There are some limitations to this model, however. In real life, the US and China could go back and forth for a very long time, choosing to do nothing at some times and choosing to retaliate at other times. For example, the game tree does not take into account China imposing a certain level of tariffs now, and then sometime in the future taking more drastic measures which could be more damaging to the US. There are theoretically an infinite number of different policy changes at different points in time, so no game tree can account for every single possibility. However, this game tree does show the simple, fundamental conflict happening now, and is reasonably accurate in showing what is happening at the moment, so it does accurately show what general action the US should take.

 

For Ohio steel workers, this means that they should vote for and support politicians who are willing to take protectionist measures. Although this may only mildly help (the payoff is only 2, and other industries may be mildly held back) it does improve the status quo assuming China doesn’t fully retaliate.

 

Sources:

1- http://money.cnn.com/2016/06/30/news/economy/college-grads-jobs/index.html

2- https://www.economist.com/news/special-report/21707834-truth-and-myth-about-effects-openness-trade-coming-and-going

3- https://www.theatlantic.com/business/archive/2017/07/made-in-america/534339/

4- https://www.reuters.com/article/us-usa-trade-steel-agriculture/trade-war-backfire-steel-tariff-shrapnel-hits-u-s-farmers-idUSKBN1HK0GV

5- https://www.economist.com/news/leaders/21737517-it-bet-china-would-head-towards-democracy-and-market-economy-gamble-has-failed-how

 

 

Share this project
COMMENTS: 1
  1. April 30, 2018 by Anderson Page

    Wow – great project. To be honest, I got a little lost with all the math, but what a cool way to look at economics. I have never really thought of economics in that way, and while I was definitely confused at times, I like the way you presented it. Your explanations were clear and thorough. I personally find game theory incredibly interesting, and what a cool way to apply it! Again, really interesting and intelligent idea. Great job!

Sorry, the comment form is closed at this time.

Sorry, the comment form is closed at this time.