Harsanyi%20transformation

1
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.

2
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).

3
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).