Game Theory for 14-Year-Olds

What is game theory?

Game theory is a way of thinking about how to choose the best result for yourself by predicting the actions of others. It might sound difficult, but there are many situations in everyday life where we use game theory.

For example,

• When playing rock-paper-scissors with a friend, you predict what move they might make and decide on your own move.

• When a store is having a sale, you think about how much other people want the items you want to buy, and then decide whether or not to buy them yourself.

• In a soccer match, you read the opposing team's movements and decide where to pass the ball.

These can also be said to use game theory in a broad sense.
In game theory, these kinds of "mutually influential situations" are analyzed using mathematics.

1. Key points of game theory

There are two important points to consider in game theory:

(1) Everyone is looking for the best result for themselves
Everyone participating in the game tries to make the choice that will be most beneficial to them.

(2) The other party is thinking the same way as you
You make your choice while taking into account that the other party is also acting in pursuit of the best result for themselves.

Game theory is about finding the optimal choice for yourself by considering these two points.

2. Various algorithms included in game theory

There are many "algorithms (procedures or methods for solving problems)" in game theory.
Here, I will introduce a few representative ones.

(1) Nash Equilibrium

This is a state where, no matter what action the other party takes, changing your own choice further will not result in any gain (the current state is the best).
In other words, it is a state where "after predicting the other party's actions, there is no better choice for you (it won't get any worse)."
It is believed that when everyone reaches a Nash equilibrium, the situation stabilizes.

[Main fields of application]

• Economics
It is used when companies engage in price competition or decide on production volumes, helping them predict the actions of other companies to develop optimal strategies.

・Political Science
Used to analyze negotiations between countries and strategies in elections.

【Practical Examples】

・Prisoner's Dilemma
A famous example showing that when two criminals are caught, the outcome may not be the best for both depending on whether they confess or remain silent.
In fact, both confessing can sometimes lead to a worse outcome.

・Chicken Game
A game where two cars drive toward each other and compete to see who will swerve first.
If neither swerves, they will collide, but since swerving first means losing, this situation allows us to consider the Nash equilibrium.

(2) Minimax Algorithm

An algorithm that considers the worst-case scenario and acts to achieve the best possible result within that context.
It is a method of choosing an action by assuming that "the opponent will definitely move in a way that is most disadvantageous to me," while still ensuring you do not suffer the greatest loss.

【Main Fields of Application】

・Computer Games (especially board games)
Used in computer programs for chess or shogi to predict the opponent's next move and make a move that prevents you from losing.

・Decision Making
Used when planning for disaster prevention or risk management by assuming the worst-case scenario.

【Practical Examples】
・Tic-Tac-Toe AI
When a computer plays Tic-Tac-Toe, the Minimax algorithm is used to calculate all possible next moves for the opponent and place its mark in a square that prevents it from losing.

(3) Subgame Perfect Equilibrium

A state where there is a Nash equilibrium at each stage (called a "subgame") when a game is divided into several stages.
It is a way of thinking that involves making the best choice now by anticipating future actions.

【Main Fields of Application】

・International Negotiations
Used to analyze strategies for negotiations that take place over multiple stages from a long-term perspective.

・Corporate Strategy
Used when developing business strategies that involve multiple steps, from new product development to sales.

【Practical Examples】

・Market Launch of a New Product
This applies to cases where a company considers whether to launch a new product, including how competitors might react and how the company itself will act in the subsequent stages.

(4) Folk Theorem

A theorem showing that when a game is repeated many times, there are many cases where cooperation leads to a good result for everyone.
Even if a Nash equilibrium is not reached in a one-time game, better results can be obtained by cooperating with each other in repeated games.

【Main Fields of Application】

・Repeated transactions and negotiations
　It is used to analyze how cooperative relationships emerge in situations where relationships continue over time, such as long-term business transactions between companies or diplomatic negotiations between countries.

・Social contract
　It is sometimes used to explain the importance of people cooperating and following rules within a society.

[Actual examples]

・Management of fishery resources
　You can consider a situation where if all fishermen cooperate by not overfishing, they will be able to continue catching fish in the future.
　If everyone thinks only of themselves and overfishes, there is a possibility that the fish will disappear.

Conclusion

　Game theory is a very interesting field of study that analyzes how to achieve the best results by carefully considering your own actions and those of others.

　There are many situations in everyday life where you can use the concepts of game theory, so please try looking at the events around you from the perspective of "game theory"!

PS
"How to win by playing games with AI"

　AI thinks about its moves based on the premise that "the opponent is also acting in search of the best result for themselves."
　So, if you try to "outsmart" it by making a "bad move," it might unexpectedly "panic" and make a strange move.
　Well, the outcome is usually that you get soundly defeated.