Perfect Bayesian Equilibrium
A refinement for dynamic games of incomplete information pairing strategies with beliefs.
Definition
A PBE is such that (i) each is sequentially rational given beliefs and (ii) is updated via Bayes' rule on the equilibrium path (and reasonably off-path).
Stronger refinements include sequential equilibrium (Kreps-Wilson) which requires beliefs to be the limit of fully mixed strategies.
Intuition
Beliefs are an integral part of the solution — players best-respond given what they believe about private information at each decision point.
It is the natural refinement for signaling and reputation games.
Worked example
In Spence's signaling model, a PBE involves high-ability workers choosing education levels that low-ability workers would not imitate.
Separating and pooling equilibria in signaling games are classified by PBE.
The math
Sequential equilibrium strengthens PBE by requiring consistent beliefs via a trembling approximation.
Intuitive criterion (Cho-Kreps) further refines signaling equilibria via off-path belief restrictions.
Where it is used
Job-market signaling, reputation models, bargaining under incomplete information, and cheap talk.
Used to analyze dynamic corporate finance and political-economy models.
More in Game theory
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