Summary: Evolutionary game dynamics of mixed-strategy distributions typically exhibits continua of stationary states. We introduce a dynamical model of mutation in evolutionary games, in which all possible mixtures of \(n\) pure strategies are admitted. Although mutation generates random variability, its effect on the dynamics is to dissolve continua of neutrally stable equilibria into isolated, asymptotically stable ones. Unbeatability, i.e., uniform neutral stability, of strategies is related to the dynamic behavior under mutation, which is used to characterize the Nash condition. Simple conditions on the payoff ensuring global stability are specified, and the case of \(n= 2\) pure strategies is investigated in detail.