I have recently come across the term forward / backward looking refinement of a Perfect Bayesian Equilibrium. I am, however, unsure about the meaning of this term, and unable to find any information about this. Does anyone know the difference between the two? For instance, is a PBE refined with Intuitive Criterion a PBE with forward looking refinement (as the IC makes a statement about how beliefs should be influenced by off-equilibrium-path actions, and thus influences plays in further periods)? If so, what would be an example for a backward looking refinement?
2026-05-05 23:52:27.1778025147
Categorization of PBE refinements into forward/backward looking?
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The usual examples are backward induction and forward induction. Somewhat surprisingly, backward induction is forward looking and forward induction is backwards looking.
In backward induction you start at the end of the game- which lies in the future. So it is forward looking. Forward induction, which has many differen definition, uses reasoning based on a player having arrived at a node because another player in the past did something for some reason, so it looks backward.
I would not think too much about forward and backward looking behavior, it is often not that illuminating. As a matter of fact, the intuitive criterion was initially derived by Cho and kreps from (Kohlberg-Mertens-)strategic stability, which is a refinement in terms of the normal form.