Perfect Bayesian equilibrium
Strategies and beliefs that fit together, so that beliefs follow from the strategies wherever they can and every player acts optimally from every point they might find themselves at.
Often misread asSupposing the updating requirement pins beliefs down everywhere, when at information sets the strategies reach with probability zero it says nothing at all, and the modeller may choose whatever beliefs make the equilibrium work.
How to see it
Strategies and beliefs holding each other up
Two things are solved at once: what each player does, and what each believes at every point where they are unsure. Beliefs must follow from the strategies by ordinary updating wherever updating has anything to work with, and everyone must be acting optimally given their beliefs, from every point, including points the equilibrium says are never reached.
The checkOff the path, perfect Bayesian imposes almost no discipline on beliefs. That freedom is exactly the hole that sequential equilibrium and the intuitive criterion were built to close.
Try itFind a signalling equilibrium held up by the off path belief that any deviator is surely the strong type, and check it is a perfect Bayesian equilibrium. Then swap in surely the weak type and check again. If both survive, you have seen precisely what the concept does not do.
Games that show it
Know these first
Leads on to
Easily confused with
Sources
- Fudenberg, D. & Tirole, J. (1991). MIT Press.
- Gibbons, R. (1992). Harvester Wheatsheaf. Published in the United States as 'Game Theory for Applied Economists', Princeton University Press.
- Mas-Colell, A., Whinston, M. & Green, J. (1995). Oxford University Press.