Harsanyi transformation Players have private information Each possibility is called a type. Nature chooses a type for each player. Probability distribution common knowledge. A strategy for each player prescribes a strategy for each possible type.

Bayesian Nash Equilibrium (BNE) Propose a strategy profile (possibly mixed). See how players update their believes accordingly (Bayes’ Theorem). Check that players play a best response given these updated beliefs (Nash condition).

Perfect Bayesian Equilibrium (PBE) Strategy profile and beliefs for every information set s.t. The strategies of the game are Nash given all beliefs and strategies; Where possible, beliefs are obtained from Bayes’ Theorem (i.e. beliefs are rational) Bayes’ theorem cannot be applied at info sets that are off the equilibrium path (those that occur w.p. 0).