Game Theory

Game theory is a branch of mathematics that studies strategic decision making. It can be applied to a wide range of situations, from economic markets to political conflicts to game design. In game theory, there are two main types of games: deterministic and stochastic.

Deterministic games are those in which the outcome is certain based on the actions of the players. For example, in a game of chess, the outcome is determined by the moves of the players, and there is no element of chance. On the other hand, stochastic games include an element of chance, such as the roll of a die or the flip of a coin.

In addition to these two types of games, game theory also distinguishes between “full information” and “partial information” games. In full information games, all players have complete knowledge of the game state and the actions of the other players. In contrast, in partial information games, some players may not have complete information about the game state or the actions of the other players.

One of the key features of game theory is that it can be used to analyze the behavior of players over time. In the first time a game is played, there may be a lot of uncertainty about the outcome. However, as the game is played multiple times, the behavior of the players becomes more predictable and the game becomes more deterministic. This is known as the “repeated game” concept.

An example of a game that can be analyzed using the repeated game concept is the classic video game “Mario.” As players become more familiar with the game and learn the different levels and obstacles, their behavior becomes more predictable and the game becomes more deterministic.

In recent years, game theory has been applied to the field of artificial intelligence, with AI systems using concepts such as Nash equilibrium and GTO (game-theoretic optimal) play to improve their performance in games such as poker, Go, and Mahjong.

Beyond traditional games, game theory can also be applied to other types of competitions and events, such as sports and real-time strategy games. These situations require a certain level of “mental toughness” in order to make effective decisions under pressure. Training in game theory can benefit individuals in their personal and professional lives by helping them develop the ability to think strategically and make decisions with a long-term perspective.

Ultimately, the goal of game theory is to maximize expected value (EV) for the players. This means considering all possible outcomes and determining the most likely result based on the actions of the players. By understanding the concepts of game theory and applying them to different situations, individuals can improve their decision-making skills and increase their chances of success in various areas of life.

tags:

  • [[Mathematics]]
  • [[Economics]]
  • [[Mental Toughness]]
  • [[Psychology of Competition]]
  • [[李永乐老师]]
  • [[Nash Equilibrium]]