What is bayesian games?

Bayesian games are a type of game theory in which the players have incomplete or imperfect information about the game they are playing. In other words, each player has some private belief about the other player's strategy or the value of the game parameters. The term "Bayesian" refers to the notion that each player updates their belief based on new information they receive during the course of the game.

Bayesian games are typically modeled using probability theory, where each player's belief is represented by a probability distribution over the set of possible strategies or outcomes. The players then use these probabilities to make optimal decisions given their incomplete information.

One of the key challenges in analyzing Bayesian games is the need to calculate the players' expected utilities under different possible beliefs. This often requires Bayesian inference techniques, which can be computationally demanding.

Bayesian games have many real-world applications, such as in auctions, bargaining, and negotiation. They are also commonly used in machine learning algorithms, particularly in the field of reinforcement learning.