Example
The game represented in the following normal form matrix has two pure strategy Nash equilibria, namely
| Left | Right | |
| Up | 1, 1 | 2, 0 |
| Down | 0, 2 | 2, 2 |
| Trembling hand perfect equilibrium | ||
Assume player 1 is playing a mixed strategy, for . 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 and maximal weight on L. By symmetry, player 1 should place a minimal weight on D if player 2 is playing the mixed strategy . Hence
However, similar analysis fails for the strategy profile
Assume player 2 is playing a mixed strategy . Player 1's expected payoff from playing U is:
Player 1's expected payoff from playing D is:
For all positive values of ε, player 1 maximizes his expected payoff by placing a minimal weight on D and maximal weight on U. Hence
Read more about this topic: Trembling Hand Perfect Equilibrium
Famous quotes containing the word example:
“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)