Perfect Equilibrium

A mixed profile $\sigma\in\Sigma$ is a perfect equilibrium of a finite normal-form game if there are completely mixed profiles $\sigma^n\in\operatorname{int}\Sigma$ and numbers $\epsilon_n\to 0$ such that:

• each $\sigma^n$ is $\epsilon_n$-perfect;
• $\sigma^n\to\sigma$.

Thus a perfect equilibrium is a limit of equilibria of games in which every pure strategy has positive tremble probability and non-best responses vanish in the limit.

References

• [MFoGT, Def. 6.5.2] Laraki, Renault, and Sorin, Mathematical Foundations of Game Theory. Selten perfect equilibrium as a limit of epsilon-perfect completely mixed profiles.