Game theory is a mathematical tool that analyzes how individuals or groups of people make decisions in strategic situations. It is applied in various fields, including economics, political science, psychology, and biology.

Game theory classifies games based on several criteria like the number of players, the information available to them, and their strategies. In this article, we will explore the different classifications of game theory.

## Classifications of Game Theory

### 1. Number of Players

Games can be classified based on the number of players involved. They can be one-player games or multi-player games.

One-player games are also known as single-person games or decision problems. In these types of games, only one player is involved and makes decisions based on a set of rules and objectives.

On the other hand, multi-player games involve two or more players who interact with each other strategically to achieve their objectives. Multi-player games can further be classified into two categories: cooperative and non-cooperative.

#### Cooperative Games

In cooperative games, players work together to achieve a common goal. They share information and resources and coordinate their actions to maximize their collective payoff. Examples include joint ventures, partnerships, and alliances.

#### Non-Cooperative Games

Non-cooperative games are those where players act independently without any communication or coordination with each other. Each player strives to maximize their payoff without considering the impact on others’ payoffs. Examples include poker, chess, and most business situations.

### 2. Information Available

Games can be classified based on the information available to each player during the game. They can be classified as complete information or incomplete information games.

#### Complete Information Games

In complete information games, each player has full knowledge about all aspects of the game such as the rules, payoffs, strategies available to other players, and the order of play. Examples include tic-tac-toe and chess.

#### Incomplete Information Games

In incomplete information games, players do not have complete information about the game. They may not know the payoffs, strategies available to other players, or even the order of play. Examples include poker and most business situations.

### 3. Strategies

Games can also be classified based on the strategies available to each player during the game. They can be classified as pure strategy or mixed strategy games.

#### Pure Strategy Games

In pure strategy games, each player has a set of actions they can take, and they choose one action that will lead to their maximum payoff. For example, in rock-paper-scissors, each player chooses one of three options without any randomness.

#### Mixed Strategy Games

In mixed strategy games, players choose their actions randomly according to a probability distribution. For example, in poker, players choose their actions based on the probability of getting a certain hand.

## Conclusion

Game theory is a powerful tool for analyzing strategic interactions between individuals or groups. It offers various classifications based on different criteria such as the number of players involved, information available to them, and strategies they can use during the game. Understanding these classifications can help us better analyze real-life situations where strategic decision-making plays an important role.