Extensive form game

Okay kiddo, imagine you and your friend are playing a game together. It's a special kind of game that you and your friend will be taking turns making decisions. This kind of game is called "extensive form game" because it shows all the possible decisions and outcomes that can happen in the game.

Now let's draw a picture of this game. First, we draw a big circle at the top to show that this is where the game starts. Inside the circle, we write down all the possible things you and your friend can do. For example, you can choose to play with your toys or your friend can choose to paint a picture. These are called "decision nodes."

Next, we draw lines coming out of each decision node, these lines represent the choices after each player gets to decide what to do. For example, if you decided to play with your toys, the line from your decision node will lead to another decision node that shows all the possible toys you can play with.

Now, when you make a decision, you have to keep in mind that your friend will get to make her own decision too. So we draw another set of decision nodes further down the lines to show what your friend can do. This is called "subgame" because this is like a smaller game within the bigger game.

Finally, we reach the end of the lines where we show the final outcome of the game or "terminal nodes." So, if you and your friend chose to play with your toys, the final outcome would be "happy playtime." Or if your friend decided to paint a picture, the final outcome would be "beautiful artwork."

So, an extensive form game is basically a way of showing all the possible decisions and outcomes of a game involving different players. By looking at the picture of the game, you can see all the possible ways the game can be played, and you can choose the best strategy for yourself. Simple, right?