In this study, we consider dynamic games with noisy signals in which any signal is possible in equilibrium due to noises in observations. We argue that in games with noisy signals, the consistency condition of beliefs required by the perfect Bayesian equilibrium or sequential equilibrium is too strong to comprehend reasonable outcomes. Accordingly, we propose alternative solution concepts called e -perfect Bayesian equilibrium and limit perfect Bayesian equilibrium. The two equilibrium concepts rely on a weaker consistency condition that requires beliefs to be updated by Bayes’ law only if the likelihood that a signal occurs given that the equilibrium action was played exceeds e > 0 . Our concepts are consistent with empirical observations that show higher deviations from Bayes’ law for rare events. We show that under some conditions, both e -PBE and limit PBE can fully recover the first-mover advantage that disappears with even a slight noise in observing the first mover’s strategy.