Epsilon-equilibria of perturbed games

We prove that for any equilibrium of a continuous (Bayesian) game, and any sequence of perturbations of that game, there exists a corresponding sequence of εequilibria converging to the given equilibrium of the original game. Thus, any equilibrium selection argument that is based on perturbations to a game is not robust to slight perturbations in best reply behavior (or to underlying preferences). This applies to many standard equilibrium selections, including Selten’s (1975) definition of trembling hand perfect equilibrium, Rubinstein’s (1989) analysis of the electronic mail game, and Carlsson and van Damme’s (1993) global games analysis.