Uncertainty in Games

Game Theory · Axiom Academy

What happens when players don't know everything about the game they're playing? In many real-world strategic situations, you don't know everything. Let's start by exploring what can be hidden in a game. What could be hidden in a strategic game? One of the most important sources of uncertainty is not knowing what type of opponent you're facing. Adjust the slider to explore different player types. Try different probabilities to see how uncertainty about player types affects the game. Now let's play! Your opponent is either Aggressive or Cautious, but you don't know which. Make your choice: Attack or Defend? When you observe your opponent's actions, you can update your beliefs about their type. This is where Bayes' rule enters game theory! Adjust your initial belief, then observe an action to see how beliefs update. Games can have incomplete information about opponent types, previous moves, or nature's random choices. This creates fundamentally different strategic problems than perfect information games. When facing uncertainty, players form beliefs represented as probability distributions over possible states. Strategy involves maximizing expected payoffs under these beliefs. As players observe actions, they update their beliefs using Bayes' rule. This creates a dynamic game where information revelation changes strategic calculations over time.

This is the written version of the interactive lesson above. See the full Game Theory course.