We characterize the essential stability of games with a continuum of players, where strategy profiles may affect objective functions and admissible strategies. Taking into account perturbations defined by a continuous mapping from a complete metric space of parameters to the space of continuous games, we prove that essential stability is a generic property and every game has a stable subset of equilibria. These results are extended to discontinuous large generalized games assuming that only payoff functions are subject to perturbations. 

We apply our results in an electoral game with a continuum of Cournot-Nash equilibria, where the unique essential equilibrium is that in which only politically engaged players participate in the electoral process. In addition, employing our results for discontinuous games, we determine stability properties of competitive prices in large economies.