Consider the following classification of solution concepts
║ static dynamic ║ ==================+===================+========================+ perfect info. ║ Nash equil. | subgame perfect equil. ║ +-------------------+------------------------+ incomplete info. ║ Bayes Nash equil. | perfect Bayes equil. ║ ==================+===================+========================+
I am wondering where Bergemann and Morris' Bayes correlated equilibrium fits in this table.
Based on the name, it seems that Bayes correlated equilibrium (BCE) is the incomplete information analogue of correlated equilibrium (a solution concept for static games), which seems to imply that BCE is a solution concept for the class of static, incomplete information games (lower left spot of the table).
The discussion in the Bergemann and Morris paper is focussed on how "signals" influence players' beliefs throughout a game. As far as I understand, signaling is only a concept that appears in dynamic games of incomplete information, which seems to imply that BCE is a solution concept for dynamic games of incomplete information (lower right spot).
Furthermore, the following statement on page 5 of the same paper states:
Lehrer, Rosenberg, and Shmaya (2013) study solution concepts which are intermediate between Bayes correlated equilibrium and Bayes Nash equilibrium, and provide partial characterizations of how the set of equilibrium outcomes vary with the information structure.
The topic of the Lehrer paper is again related to signaling. This seems to further imply that BCE is a solution concept for dynamic games.
Question: Is Bayes correlated equilibrium a relevant solution concept for dynamic games of incomplete information? If not, has anyone generalized the notion to dynamic games?