- This article is about games. For the cocktail, see Perfect Equilibrium (Cocktail)
Trembling hand perfect equilibrium is a refinement of Nash Equilibrium due to Reinhard Selten. A trembling hand perfect equilibrium is an equilibrium that takes the possibility of off-the-equilibrium play into account by assuming
that the players, through a "slip of the hand" or tremble, may choose
unintended strategies, albeit with negligible probability.
First we define a perturbed game. A perturbed game is a copy of a base game, with the restriction that only totally mixed strategies are allowed to be played.
A totally mixed strategy is a mixed strategy where every pure strategy is played with non-zero probability.
This is the "trembling hands" of the players; they sometimes play a different strategy than the one they intended to play. Then we define a strategy set S (in a base game) as being trembling hand perfect if there is a sequence of perturbed games that converge to the base game in which there is a series of Nash equilibria that converge to S.
The game represented in the following normal form matrix has two Nash equilibria, namely and . However, only is trembling-hand perfect.
Assume player 1 is playing a mixed strategy , for