Bayesian Nash equilibrium
Let's say you and your friend want to play a game with crayons. At the start of the game, you both have a secret crayon in your hand. You don't know what crayon your friend has, and your friend doesn't know what crayon you have.
Now, you have a goal in this game. You want to choose the crayon that matches the color your friend has. But how can you do that when you don't know what crayon your friend has?
To make this game fair, you need to use something called Bayesian Nash Equilibrium. It's like using special rules to help you make the best decision when you don't have complete information.
Here's how it works: You start by guessing which color crayon your friend has. Let's say you guess red. Then, you think about what crayon you should pick based on this guess. You might choose to pick a red crayon too, in the hope that your guess was correct.
But what if your friend guessed that you would guess red? They might choose a different color crayon to try and trick you. So, you try to think about what your friend might do based on what you would do.
To do this, you need to think about what you both know about each other. You know that your friend wants to match the colors, just like you do. So, you both have this common goal in mind.
Using Bayesian Nash Equilibrium means that you need to think about the probabilities, or likelihood, of each crayon being chosen. You consider how likely it is for your friend to have a certain color crayon, based on what you know about them.
For example, let's say you have seen your friend use a blue crayon in the past more often than any other color. This means the probability or likelihood of your friend having a blue crayon might be higher.
So, you might decide to guess blue, thinking that there's a higher chance your friend has a blue crayon too. And based on this guess, you might choose to pick a blue crayon as well.
But remember, your friend also knows about this Bayesian Nash Equilibrium. They also know that you might think they have a higher chance of having a blue crayon. So, they might try to trick you by choosing a different color.
This goes back and forth until both of you make your final decisions. And then, you reveal your crayons to see if you matched or not!
Bayesian Nash Equilibrium is all about using probabilities and thinking about what the other person might do, even when you don't have all the information. It helps you make the best decision based on what you know and what you think the other person might do.
Now, you have a goal in this game. You want to choose the crayon that matches the color your friend has. But how can you do that when you don't know what crayon your friend has?
To make this game fair, you need to use something called Bayesian Nash Equilibrium. It's like using special rules to help you make the best decision when you don't have complete information.
Here's how it works: You start by guessing which color crayon your friend has. Let's say you guess red. Then, you think about what crayon you should pick based on this guess. You might choose to pick a red crayon too, in the hope that your guess was correct.
But what if your friend guessed that you would guess red? They might choose a different color crayon to try and trick you. So, you try to think about what your friend might do based on what you would do.
To do this, you need to think about what you both know about each other. You know that your friend wants to match the colors, just like you do. So, you both have this common goal in mind.
Using Bayesian Nash Equilibrium means that you need to think about the probabilities, or likelihood, of each crayon being chosen. You consider how likely it is for your friend to have a certain color crayon, based on what you know about them.
For example, let's say you have seen your friend use a blue crayon in the past more often than any other color. This means the probability or likelihood of your friend having a blue crayon might be higher.
So, you might decide to guess blue, thinking that there's a higher chance your friend has a blue crayon too. And based on this guess, you might choose to pick a blue crayon as well.
But remember, your friend also knows about this Bayesian Nash Equilibrium. They also know that you might think they have a higher chance of having a blue crayon. So, they might try to trick you by choosing a different color.
This goes back and forth until both of you make your final decisions. And then, you reveal your crayons to see if you matched or not!
Bayesian Nash Equilibrium is all about using probabilities and thinking about what the other person might do, even when you don't have all the information. It helps you make the best decision based on what you know and what you think the other person might do.