## An Analysis of Booming Private Tutoring Industry in South Korea Through Game Theory

According to the Ministry of Education and National Statistics Agency of South Korea, South Koreans spend about \$20 billion on private tutoring each year. This amount is bigger than many other countries’ annual spending on public education. It is true and shocking that in South Korea about ninety percent of elementary students receive private tutoring. Popular subjects include English and Mathematics. Some popular tutors earn \$5 million a year, and this is not surprising if one is aware of the fact that twenty percent of South Korean family’s income goes into private tutoring.

There is no doubt that South Korea is one of the highest educated nations in the world, and South Korean students achieve high academic performance in mathematics and science. Many believe that this “education” in South Korea enabled the nation’s rapid economic growth over the past sixty years (after the Korean War). However, because of the growing concerns about the extreme competition, decreasing birth rate (as the costs of educating children rise significantly), and a high suicide rate, in 2009 the South Korean government began enforcing a curfew.

The purpose of this post is to examine South Korea’s booming private tutoring industry through game theory, which is designed to analyze situations where one person’s decisions not only depend on his options but also on others’.

Suppose Angela(A) and Blair(B) know each other because their sons go to the same high school. In this game, players are Angela(A) and Blair(B). Their strategies include PT(private tutoring) or NPT(no private tutoring) for their sons. The payoff is the benefit of mother from her son’s class rank minus the cost of private tutoring.

(Assume income levels and academic abilities are similar)

Higher Class Rank (+10)

Lower Class Rank (-10)

Same Class Rank (0)

Cost of Private Tutoring (-5)

If A’s son does not receive private tutoring, then B will make her son receive private tutoring so that he can rank higher than A’s son. In this situation, Angela’s payoff is -15(cost of private tutoring[-5] + lower class rank[-10]), while Blair’s payoff is +5(cost of private tutoring[-5] + higher class rank[+10]). Similarly, if B’s son does not receive private tutoring, then A will make her son receive private tutoring so that he can rank higher than B’s son. This explains why the private tutoring industry has been rapidly expanding.

In this game, both A and B have a dominant strategy, which is using “PT.” For Angela, it is always better to make her son receive private tutoring regardless of Blair’s decision (∵ 5>0 and -5>-15). Due to the same reason, it is always better for Blair to make her son receive private tutoring. Therefore, the Nash equilibrium, in which players optimize individually, is at (-5, -5) when both A and B use strategy PT.

Although the Nash equilibrium indicates that each player is playing her best, there is a better outcome (0,0) for both players. In other words, if both A and B play NPT, there is a higher combined payoff 0>-10 than both play PT. If we think intuitively, this phenomenon makes sense. Without private tutoring, Angela and Blair can save their money and their sons will perform equally. If A and B can agree on what they should do to maximize their benefits, this optimal choice (0, 0) can be achieved; however, in reality, if one betrays and switches to PT strategy, this optimal choice becomes impossible. Probably the government’s curfew and other efforts to restrict PT industry can be interpreted as a compulsory method to reach this optimal choice of strategies.

Developing a game theory model of South Korea’s private tutoring industry enabled us to understand why the private tutoring industry has grown rapidly and enormously. In addition, it suggested an existence of socially better (more optimized) outcome, as well as the possible explanation for the government’s action and its consequence. Although this game theory model tells significant materials, we need to consider many other variables to determine whether the government’s intervention betters the society.

Sources

https://www.washingtonpost.com/world/s-korea-tries-to-wrest-control-from-booming-private-tutoring-industry/2011/01/12/AFNXQfXC_story.html

http://blogs.wsj.com/korearealtime/2014/11/04/what-ails-south-koreas-education-system-private-tutoring-says-world-bank-chief/