Hearing that a neighbor has added another private academy to their child’s schedule makes one feel anxious for no reason.
In 2025, the cost of private education for elementary, middle, and high school students was 27.5 trillion won. This structure, where everyone would be better off if they all cut back, yet an individual suffers if they cut back alone, is known as the Prisoner’s Dilemma. The state where everyone’s rational choices become locked in is called a Nash Equilibrium.
What is a ‘Game’ in Game Theory?
While the name “game theory” might sound like it relates to computer games or board games, the term “game” here has a much broader meaning.
It refers to strategic situations where multiple people make decisions, and each person’s choice affects the others. Rock-paper-scissors to decide who pays for lunch, a football penalty kick, price competition between companies, and trade wars between nations are all games.
The core feature of a game situation is that my best choice depends on the other person’s choice.
In rock-paper-scissors, “what is the best move to make” depends on what the opponent plays. Optimization, the primary tool of classical economics, is weak in such situations. It is powerful in scenarios where you only need to focus on yourself, like a consumer maximizing satisfaction based on income and prices, but it loses its effectiveness the moment choices become intertwined. This is why research into oligopolistic markets, where a small number of firms compete, was slow for a long time despite its importance. Game theory broke through this barrier and expanded the horizons of 20th-century economics.
The Three Ingredients of Game Theory: Players, Strategies, and Payoffs
No matter how simple a strategic situation is, it must contain three elements: players, strategies, and payoffs.
Let’s imagine Person A and Person B playing rock-paper-scissors to decide who buys lunch.
The decision-makers, A and B, are the players. The rock, paper, and scissors they can choose are their strategies. The payoff is the satisfaction each player gains from the game’s outcome—in this case, the feeling of getting a free lunch versus having to pay for it. While complex situations may require additional elements like information or timing, no game exists without these three.
Nash Equilibrium, a State No One Wants to Change Alone
What game theory ultimately seeks to know is “what will happen.”
In 1950, mathematician John Nash provided an answer to this question with the concept of equilibrium.
A state where every player correctly predicts the strategies of the others and makes the optimal choice accordingly is called a Nash Equilibrium.
In a Nash Equilibrium, since everyone is already doing their best given the other’s choice, no one has any reason to change their behavior alone. Thus, the state remains stable.
Conversely, if it is not a Nash Equilibrium, at least one person wants to move to a different choice, so the state cannot last long.
With this concept as a starting point, game theory grew explosively and began to be used in economics, social sciences, and even natural sciences like biology. John Nash’s life was made into the movie A Beautiful Mind, and it is fair to say his life was even more dramatic than the film.
The Prisoner’s Dilemma, Why Being Smart Leads to Collective Loss
The Prisoner’s Dilemma illustrates the Nash Equilibrium most clearly.
Person A and Person B are arrested on suspicion of a crime. The circumstances clearly point to their guilt, but without physical evidence, a confession is needed. The police keep them in separate rooms to prevent them from colluding and make the following offer: if both confess, they each get 3 years in prison; if both deny it, they get 1 year for a lesser charge; if only one confesses, the confessor goes free while the denier gets 10 years.
Prisoner’s Dilemma Payoff Matrix (Values in parentheses are payoffs for A and B, respectively; unit: years in prison)
| A \ B | B Denies | B Confesses |
|---|---|---|
| A Denies | (-1, -1) | (-10, 0) |
| A Confesses | (0, -10) | (-3, -3) |
Let’s look at the scenarios from A’s perspective.
If B confesses, A is better off confessing (3 years) than denying (10 years). If B denies, A is better off confessing (goes free) than denying (1 year). Regardless of what B does, confessing is advantageous for A. Since B is in the exact same position, confessing is also advantageous for them. Therefore, both confessing becomes the Nash Equilibrium, and the result is 3 years for each.
However, if you look at the table again, both denying results in only 1 year each, which is far better. The problem is that this cell cannot be a Nash Equilibrium. Even if they promise to deny to the end, if the other person keeps the promise, I benefit by confessing and going free, so the promise cannot hold.
What is most worth reflecting on in this result is the cause of the inefficiency.
It is not because A and B are foolish that they spend 3 years in prison. Rather, they are trapped there precisely because they are too smart and rational. Economics once held an implicit belief that if rational individuals each did their best, the result for society as a whole would also be efficient; the Prisoner’s Dilemma put a major crack in that belief.
From Arms Races to Private Education Costs, the Prisoner’s Dilemma in Reality
If this structure only existed in laboratories, there would be no need to worry. Reality is full of situations that resemble the Prisoner’s Dilemma.
A classic example is the arms race between two hostile neighboring countries, A and B.
If A increases its military spending, B must increase its own to keep up, and even if A doesn’t increase it, B is likely to increase it anyway to gain an advantage. In the end, both increase their military spending, the balance of power remains the same as before, and only the money disappears inefficiently. If that money had been spent on something like welfare, both would have been better off.
Competition for private education has the same framework.
According to the 2025 survey on private education costs for elementary, middle, and high school students by the Ministry of Education, the total expenditure was 27.5 trillion won, a 5.7% decrease from the previous year’s 29.2 trillion won, and the participation rate also dropped by 4.3 percentage points to 75.7%. However, the average monthly expenditure per student receiving private education actually increased by 2.0% to 604,000 won. This means that even as the number of students and participating households decreases, the households remaining in the competition have moved toward spending more.
If every household cut back simultaneously, children’s relative standing would remain the same while saving both money and time, but the fear of falling behind if only one household cuts back prevents this. Competition for specs among college students and protectionist trade policies between nations follow a similar structure.
Therefore, breaking such inefficiencies usually requires a mechanism that binds everyone simultaneously. This could be mandatory regulations, restrictions, or in the case of an arms race, disarmament treaties. The Prisoner’s Dilemma has already shown us that promises alone cannot hold.
Why Empathy is the Starting Point of Game Theory
Game theory allows us to predict what will happen in situations where multiple people pursuing their own interests are intertwined.
The core of Nash Equilibrium is that everyone is doing their best in response to others’ choices, and to do that, one must accurately read what the other person will choose.
Stepping into the other person’s shoes—empathy—is essentially the first step of game theory.
It is the same when facing the Prisoner’s Dilemma. If you understand why you want to confess, you can see why the other person wants to confess, and only then do you reach the conclusion that a mechanism to bind both parties simultaneously is necessary.