Game Theory

Game theory is a branch of economics that mainly studies various behaviors of competitive or confrontational objects under certain rules. Game theory considers the predicted and actual behavior of individuals in a game and studies their optimization strategies.

In layman's terms, game theory mainly studies the strategies of multiple players in a game.

The definition of fair combination game (Impartial Game) is as follows:

The game involves two people, who take turns making decisions, and both parties know complete information about the game;

The set of decisions that any player can make in a certain state is only related to the current state and has nothing to do with the player;

The same state in the game cannot be reached multiple times. The game ends when the player is unable to act, and the game will definitely end in a non-tie after a limited number of steps.

The difference between an unfair combination game (Partizan Game) and a fair combination game is that in the unfair combination game, the set of decisions that the player can make in a certain state is related to the player. Most board games are not fair combination games, such as chess, Chinese chess, Go, backgammon, etc. (because neither side can use the other party's pieces).

The Misère Game is played according to traditional game rules, but the winner is the first player to be unable to act. Take the Nim game as an example. In the Nim game, the person who takes the last stone is the winner, while in the abnormal Nim game, the person who takes the last stone is the loser.