This is a chapter from Jim Ratliff's Graduate-Level Game-Theory Course. See outline for the entire course. I no longer maintain, update, or correct these notes. However, I would appreciate hearing from people who download these notes and find them useful. Also I may eventually post problem sets and their solutions. Let me know if you'd like to be notified of such changes. (Please email me.)
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We have seen that Nash equilibria of extensive-form games can be undesirable because they can rely on incredible threats at off-the-equilibrium-path subgames. We were sometimes able to refine away such undesirable equilibria by strengthening our solution concept--demanding subgame perfection, which requires that the restriction of a strategy profile to any subgame be a Nash equilibrium of that subgame.
I offer an example extensive-form game to demonstrate that subgame perfection will not eliminate all undesirable equilibria of extensive-form games.
The concept of Perfect Bayesian equilibrium for extensive-form games is defined by four Bayes Requirements. These requirements eliminate the bad subgame-perfect equilibria by requiring players to have beliefs, at each information set, about which node of the information set she has reached, conditional on being informed she is in that information set.
§6.2: Perfect Bayesian Equilibria of Sender-Receiver (Signalling) Games