**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 assumingthat the players, through a "slip of the hand" or

**tremble,** may chooseunintended strategies, albeit with negligible probability.

## Definition

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.

## Example

The game represented in the following

normal form matrix has two pure strategy

Nash equilibria, namely <nowiki><Up, Left></nowiki> and <nowiki><Down, Right></nowiki>. However, only <nowiki><U,L></nowiki> is trembling-hand perfect.

Assume player 1 is playing a

mixed strategy <math>(1-epsilon, epsilon)</math>, for <math> 0<epsilon <1</math>. Player 2's expected payoff from playing L......
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