Essential Equilibrium Component

Let $C$ be a connected component of the Nash equilibrium set of a finite game $g$. The component $C$ is essential if every neighborhood $V$ of $C$ contains an equilibrium of every game in some sufficiently small neighborhood of $g$.

Equivalently, the component cannot be removed by arbitrarily small payoff perturbations.

References

• [MFoGT, Chapter 5, Def. 5.3.3] Laraki, Renault, and Sorin, Mathematical Foundations of Game Theory. Essential component of Nash equilibria.