Equilibrium Manifold

Fix finite player and action sets. The space of games is the Euclidean space of payoff tensors. The equilibrium manifold is the graph of the mixed Nash equilibrium correspondence: $$ E=\{(g,\sigma):\sigma\text{ is a Nash equilibrium of }g\}. $$

MFoGT studies the projection from this graph to the payoff space in order to understand robustness, index, and generic structure of equilibrium components.

References

• [MFoGT, Chapter 5, Section 5.3] Laraki, Renault, and Sorin, Mathematical Foundations of Game Theory. Graph of the Nash equilibrium correspondence as payoffs vary.