Belief system
A statement, for every point in the game where a player cannot tell which situation they are in, of how likely they think each one is.
Often misread asTreating beliefs as an input chosen by the modeller, so only strategies get solved for and the beliefs are picked afterwards to justify whatever was wanted.
How to see it
Beliefs are solved for, not supplied
Whenever a player must move without knowing exactly where they are, they are carrying some view of the odds on each possibility. A belief system is that view written down for every such point in the game. It is part of the answer, not part of the setup.
The checkStrategies and beliefs are determined together, and each has to be defensible given the other.
Try itIn a signalling game, point at a message the equilibrium says will never be sent and ask what the receiver thinks on seeing it. If you cannot state numbers there, your equilibrium is incomplete whatever the strategies say.
Games that show it
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.