Core (game theory)

Okay, let's imagine that you and your friend have a toy that you both really want to play with. But there's only one toy and you both can't play with it at the same time. So how do you decide who gets to play with the toy?

Here is where the idea of the core in game theory comes in. The core is a concept that helps us find a fair way to share or allocate things between people. In our case, the toy is what we want to allocate.

To find the core, we need to think about what each person wants and what they would give up to get it. Imagine that you and your friend both make a list of other toys that you would be willing to play with instead of the one toy you both want. You might have different toys on your list, but the important thing is that you both have some options.

Now, let's say you both have three other toys on your list. You look at each other's lists and see if there is any toy that both of you would be happy to play with instead of the toy you both want. If you find a toy that both of you would be satisfied with, then that toy is in the core.

But what if you can't find a toy that both of you would be happy with? Well, that means that there is no solution in the core. In other words, there is no fair way to share the toy that both of you want.

The core is useful because it helps us see if there is a compromise or agreement that would make everyone happy. It helps us find a solution that is fair and makes sure that no one feels left out or unhappy.

In summary, the core in game theory is a way of finding a fair solution or allocation when there is something that multiple people want. It helps us see if there is a compromise or agreement that makes everyone happy, or if it's just not possible to find a fair solution.