There are two possible ways of extending the definition of trembling hand perfection to extensive form game

Extensive form game

An extensive-form game is a specification of a game in game theory, allowing explicit representation of a number of important aspects, like the sequencing of players' possible moves, their choices at every decision point, the information each player has about the other player's moves when he...

s.

• One may interpret the extensive form as being merely a concise description of a normal form game and apply the concepts described above to this normal form game. In the resulting perturbed games, every strategy
  Strategy (game theory)
  In game theory, a player's strategy in a game is a complete plan of action for whatever situation might arise; this fully determines the player's behaviour...
  
   of the extensive-form game must be played with non-zero probability. This leads to the notion of a normal-form trembling hand perfect equilibrium.

• Alternatively, one may recall that trembles are to be interpreted as modelling mistakes made by the players with some negligible probability when the game is played. Such a mistake would most likely consist of a player making another move
  Strategy (game theory)
  In game theory, a player's strategy in a game is a complete plan of action for whatever situation might arise; this fully determines the player's behaviour...
  
   than the one intended at some point during play. It would hardly consist of the player choosing another strategy
  Strategy (game theory)
  In game theory, a player's strategy in a game is a complete plan of action for whatever situation might arise; this fully determines the player's behaviour...
  
   than intended, i.e. a wrong plan for playing the entire game. To capture this, one may define the perturbed game by requiring that every move
  Strategy (game theory)
  In game theory, a player's strategy in a game is a complete plan of action for whatever situation might arise; this fully determines the player's behaviour...
  
   at every information set
  Information set
  In game theory, an information set is a set that, for a particular player, establishes all the possible moves that could have taken place in the game so far, given what that player has observed. If the game has perfect information, every information set contains only one member, namely the point...
  
   is taken with non-zero probability. Limits of equilibria of such perturbed games as the tremble probabilities goes to zero are called extensive-form trembling hand perfect equilibria.

The notions of normal-form and extensive-form trembling hand perfect equilibria are incomparable, i.e., an equilibrium of an extensive-form game may be normal-form trembling hand perfect but not extensive-form trembling hand perfect and vice versa.
As an extreme example of this, Jean-François Mertens has given an example

Quasi-perfect equilibrium

Quasi-perfect equilibrium is a refinement of Nash Equilibrium for extensive form games due to Eric van Damme. Informally, a player playing by a strategy from a quasi-perfect equilibrium takes observed as well as potential future mistakes of his opponents into account but assumes that he himself...

 of a two-player extensive form game where no extensive-form trembling hand perfect equilibrium is admissible, i.e., the sets of extensive-form and normal-form trembling hand perfect equilibria for this game are disjoint.

An extensive-form trembling hand perfect equilibrium is also a sequential equilibrium

Sequential equilibrium

Sequential equilibrium is a refinement of Nash Equilibrium for extensive form games due to David M. Kreps and Robert Wilson. A sequential equilibrium specifies not only a strategy for eachof the players but also a belief for each of the players...

. A normal-form trembling hand perfect equilibrium of an extensive form game may be sequential but is not necessarily so. In fact, a normal-form trembling hand perfect equilibrium does not even have to be subgame perfect

Subgame perfect equilibrium

In game theory, a subgame perfect equilibrium is a refinement of a Nash equilibrium used in dynamic games. A strategy profile is a subgame perfect equilibrium if it represents a Nash equilibrium of every subgame of the original game...

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