Before revision:  Current literature has either characterized asymptotic behavior in general settings under the assumption that the agent's action converges (which sometimes does not) or has established convergence of the action in specific applications. By noting that the key element to predict the agent's behavior is the frequency of her past actions, we are able to characterize asymptotic behavior in general settings in terms of the solutions of a generalization of a differential equation that describes the evolution of the frequency of actions.
After revision:  Current literature has either characterized asymptotic behavior under fairly specific assumptions. By first showing that the key element to predict the agent's behavior is the frequency of her past actions, we are able to characterize asymptotic behavior in general settings in terms of the solutions of a generalization of a differential equation that describes the evolution of the frequency of actions.