Game theory is a branch of mathematics that deals with strategic decision making. It is used in a variety of fields such as economics, political science, and psychology.

In game theory, trees are used to represent the possible outcomes of a decision. A tree is a graphical representation of the different choices and their consequences.

**What is a Game Tree?**

A game tree is a visual representation of the possible outcomes of a game. It consists of nodes and branches. The nodes represent the different decision points in the game, while the branches represent the different choices that can be made at each decision point.

__How to Make a Game Tree?__

To make a game tree, you need to follow these steps:

## Step 1: Identify the Decision Points

The first step in making a game tree is to identify the decision points in the game. These are points where players have to make a choice that will affect the outcome of the game.

### Example:

Suppose you are playing a game where you have to choose between two doors – Door A and Door B. If you choose Door A, you win $1000, but if you choose Door B, you win $500.

In this example, the decision point is when you have to choose between Door A and Door B.

## Step 2: Create Nodes for Decision Points

Once you have identified the decision points in the game, create nodes for them. Nodes are represented by circles or squares.

Create two nodes for Door A and Door B.

- Node 1: Door A
- Node 2: Door B

## Step 3: Identify Possible Choices at Each Decision Point

Identify all possible choices that can be made at each decision point. These choices will be represented by branches.

At the decision point of choosing between Door A and Door B, there are two possible choices:

- Branch 1: Choose Door A
- Branch 2: Choose Door B

## Step 4: Assign Payoffs to Each Outcome

Assign payoffs to each outcome. Payoffs are the rewards or penalties associated with each choice.

If you choose Door A, you win $1000. If you choose Door B, you win $500.

- Door A: $1000
- Door B: $500

## Step 5: Connect Nodes with Branches

Connect the nodes with branches to represent the different choices and their consequences.

Connect Node 1 (Door A) with Node 2 (Door B) using branches that represent the two possible choices.

**Conclusion:**

Game trees are a useful tool for analyzing strategic decision making in games. They allow players to visualize the different choices and their consequences, which can help them make better decisions. By following these steps, you can create a game tree for any game and use it to analyze different strategies.