Chapter 4 - Bayesian Games

Abstract

Bayesian games are characterized by the fact that the data of the game are not common knowledge, allowing concepts such as private information and secret information to appear. When a player has private information, he is the only player who knows this information but all the players are aware he possesses it. On the other hand, information is said to be secret from a given player if all the other players do not know he possesses it. An important notion in Bayesian games is the notion of “type.” The data of the game are generally not known to the players. All the data that influence the utility of a player can be seen as a state of nature (the actions, the realization of a random variable). A type corresponds to a “state of mind” of a player—that is, the description of belief about the state of nature. This chapter discusses three essential reasons: first, to see the difference between what is commonly called a game with incomplete information, or Bayesian game in the game-theoretic literature and what is called a game with incomplete information in the framework of learning. Second, the framework of learning may be inapplicable, in such a case, players will not receive samples or feedbacks from their environment, preventing them from learning from experience. And the last third reason states that Bayesian games possess some special features that may lead to surprising conclusions, not encountered in games with complete information.