Consistency of beliefs
Beliefs away from the expected path count as reasonable only if they are the limit of beliefs worked out from strategies in which every move still has some small chance of being played.
Often misread asReading consistency as the weaker requirement that beliefs merely be updated correctly along the path, which every perfect Bayesian equilibrium already satisfies.
How to see it
Updating restored where there was nothing to update on
Off the expected path you can usually believe whatever you like without contradicting the arithmetic, because the arithmetic is dividing by zero. Consistency closes that off by requiring your beliefs there to be the limit of beliefs that would have been forced on you in nearby games where every move happens with some tiny chance.
The checkConsistency is about what happens off the path. It makes off path beliefs the limit of on path beliefs in perturbed games, which ties beliefs at different information sets together in a way updating alone leaves free.
Try itTake an equilibrium whose off path beliefs at two separate information sets were chosen independently to make everything work. Ask whether a single sequence of trembles could produce both at once. If not, the beliefs are inconsistent even though each one is separately legal.
Know these first
Leads on to
Easily confused with
Sources
- Kreps, D. M. & Wilson, R. (1982). Econometrica 50(4), 863-894.
- Fudenberg, D. & Tirole, J. (1991). MIT Press.
- Myerson, R. (1991). Harvard University Press.