  Finding equilibria points in continuous minimax games has become a key
problem within machine learning, in part due to its connection to the training
of generative adversarial networks. Because of existence and robustness issues,
recent developments have shifted from pure equilibria to focusing on mixed
equilibria points. In this note we consider a method proposed by Domingo-Enrich
et al. for finding mixed equilibria in two-layer zero-sum games. The method is
based on entropic regularisation and the two competing strategies are
represented by two sets of interacting particles. We show that the sequence of
empirical measures of the particle system satisfies a large deviation principle
as the number of particles grows to infinity, and how this implies convergence
of the empirical measure and the associated Nikaid\^o-Isoda error,
complementing existing law of large numbers results.
