🎲 Bayesian Games and Incomplete Information

In real life, we often make decisions without knowing everything. That's what Bayesian games are about.

🔍 What is a Bayesian Game?

A Bayesian game is a game with incomplete information. Each player has private information. This is called their type.

For example, imagine two people are playing poker. You don't know your opponent's cards. But you may have a belief about what they could have.

Bayesian games help us model this kind of situation.

Each player doesn't know everything. But they have beliefs about others.

For example:

You're selling a used phone.
You don't know how much the buyer is willing to pay.
But you guess they are either a student 💼 or a tech lover 🤓.
You believe there is a 60% chance they are a student, and 40% chance they are a tech lover.

This belief affects your pricing strategy.

Think about Amazon. It wants to set prices for you.

But it doesn't know exactly how much you are willing to pay.

Maybe it knows you are a frequent shopper. Or maybe it thinks you are just browsing.

It uses your profile (your "type") to make pricing or ad decisions.

You apply for a job. You don’t know how much the company is willing to pay.

The company also doesn’t know your true skill level.

Both sides have incomplete information.

But both try to make smart choices based on what they believe.

Bayesian games are used in:

Bayesian games are powerful tools.

They help model real-world situations where players have private info.

By using beliefs, players can still make smart choices.

Remember: just because you don’t know everything doesn’t mean you can’t play smart! 😄