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The trembling hand perfection is a notion that eliminates actions of players that are unsafe because they were chosen through a slip of the hand. Players could choose actions that are not the intended ones due (trembling) that lead to unintended outcomes. Off-the-equilibrium plays are due to trembling or mistakes in choosing the action among the action set of players.
Example
The game represented in the following normal form matrix has two Nash equilibria, namely <Top, Left> and <Bottom, Right> (<T,L> and ). However, only <T,L> is trembling-hand perfect. The term normal form is used in a variety of contexts. ...
In game theory, the Nash equilibrium (named after John Nash who proposed it) is a kind of optimal collective strategy in a game involving two or more players, where no player has anything to gain by changing only his or her own strategy. ...
| Left | Right | | Top | 1, 1 | 2, 0 | | Bottom | 0, 2 | 2, 2 | Assume player 1 is playing a mixed strategy . Player 2's expected payoff from playing L is:
Player 2's expected payoff from playing the strategy R is:
For small values of ε, player 2 maximizes his expected payoff by placing a minimal weight on R. By symmetry, player 1 should place a minimal weight on B if player 2 is playing the mixed strategy . Hence <T,L> is trembling-hand perfect.
However, similar analysis fails for the strategy profile .
Assume player 1 is playing a mixed strategy . Player 2's expected payoff from playing L is:
Player 2's expected payoff from playing the strategy R is:
For all positive values of ε, player 2 maximizes his expected payoff by placing a minimal weight on R. Hence is not trembling-hand perfect because player 2 (and, by symmetry, player 1) maximizes his expected payoff by deviating with a small chance of error.
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