Intuitive criterion
An equilibrium is thrown out if a type could credibly explain an unexpected move by pointing out that only a type who stood to gain from it would ever have made it.
Often misread asApplying it as though it wiped out pooling equilibria in general, when it only bites where some type could not possibly gain from the deviation under any response at all, and plenty of pooling equilibria survive it.
How to see it
Would that type ever have wanted to deviate
Some equilibria stand up only because of a threat to think badly of anyone who does something unexpected. The criterion asks whether that bad thought is even coherent. If the unexpected move could never pay off for the type being accused, but could pay off for another type, you should stop accusing the first one.
The checkCheck the deviation one type at a time. If every type might gain under some response the receiver could give, the criterion has nothing to say.
Try itIn an education signalling model, take a pooling equilibrium sustained by the belief that anyone studying more is a low type. Ask whether a low type could ever profit from that extra study even if the market believed them to be high. If not, you have found the belief the criterion deletes.
Games that show it
Know these first
Easily confused with
Sources
- Cho, I-K. & Kreps, D. (1987). Quarterly Journal of Economics 102(2), 179-221.
- 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.