Game theory is an interesting branch of mathematics that focuses on decision-making. It deals with the analysis of strategic interactions between different agents. In game theory, cooperative games are a type of game where players work together to achieve a common goal.

**What Are Cooperative Games?**

In cooperative games, players form coalitions and work together to achieve a common objective. The main difference between cooperative games and non-cooperative games is that in non-cooperative games, players act independently without any communication or coordination.

In cooperative games, players can communicate their strategies and plans to each other to form a coalition. The coalition then works together to achieve an objective that benefits all members.

__Types of Cooperative Games__

There are two types of cooperative games: transferable utility (TU) and non-transferable utility (NTU).

**Transferable Utility (TU) Games:**In TU games, the payoff or utility can be transferred from one player to another. For example, if two players form a coalition and win a prize of $100, they can divide the prize equally.**Non-Transferable Utility (NTU) Games:**In NTU games, the payoff or utility cannot be transferred from one player to another. For example, if two players form a coalition to win an auction for a painting, they cannot divide the painting into two pieces.

## The Core

The core is an important concept in cooperative game theory. It is the set of outcomes that are stable and cannot be improved by any other coalition. The core includes all solutions that are acceptable to all members of the coalition.

### Shapley Value

The Shapley value is a method used in cooperative game theory to distribute the payoff or utility among members of the coalition. It is based on the contribution of each player to the coalition. The Shapley value is fair and ensures that each player receives a share of the payoff that corresponds to their contribution.

**Advantages of Cooperative Games:**Cooperative games promote teamwork and collaboration. They encourage players to work together towards a common goal, which can lead to better outcomes for everyone involved.**Disadvantages of Cooperative Games:**Cooperative games require communication and coordination between players, which can be difficult to achieve. They also require trust among players, which may not always be present.

## Conclusion

Cooperative games are an interesting type of game theory that focuses on collaboration and teamwork. They offer advantages such as promoting better outcomes for all members of the coalition, but also have disadvantages such as requiring communication and trust between players.

Overall, cooperative games are an important concept in game theory that can help us understand how groups of people can work together towards a common goal.