The theory of normal form games from the differentiable viewpoint

Abstract

An alternative definition of regular equilibria is introduced and shown to have the same properties as those definitions already known from the literature. The system of equations used to define regular equilibria induces a globally differentiable structure on the space of mixed strategies. Interpreting this structure as a vector field, called the Nash field, allows for a reproduction of a number of classical results from a differentiable viewpoint. Moreover, approximations of the Nash field can be used to suitably define indices of connected components of equilibria and to identify equilibrium components which are robust against small payoff perturbations.