Trembling hand perfection
An equilibrium counts only if it survives the possibility that every player makes each mistake with some small probability, which rules out plans that rely on a move never being tried.
Often misread asTreating it as a claim that players are error prone, rather than as a stability test in which the errors are a device for making every part of the game reachable.
How to see it
No plan may rely on something being impossible
Suppose everybody occasionally slips and plays something other than what they intended, with some small probability. An equilibrium is trembling hand perfect if it still makes sense under that supposition. Plans that work only because some situation is assumed never to arise do not survive it.
The checkThe trembles are a limiting argument. The equilibrium has to survive as the mistake probabilities shrink towards nothing, and it is the surviving in the limit that matters, not the mistakes.
Try itFind a Nash equilibrium in which one player uses a weakly dominated strategy. Give the other player a one in a thousand chance of slipping, then check whether the weakly dominated strategy is still a best response. If it is not, the trembles have removed it.
Games that show it
Know these first
Leads on to
Easily confused with
Sources
- Selten, R. (1975). International Journal of Game Theory 4(1), 25-55.
- Fudenberg, D. & Tirole, J. (1991). MIT Press.
- Myerson, R. (1991). Harvard University Press.