The development of mechanisms to understand and model the expected behaviour of multiagent learners is becoming increasingly important as the area rapidly find application in a variety of domains. In this paper we present a framework to model the behaviour of Q-learning agents using the e-greedy exploration mechanism. For this, we analyse a continuous-time version of the Q-learning update rule and study how the presence of other agents and the e-greedy mechanism affect it. We then model the problem as a system of difference equations which is used to theoretically analyse the expected behaviour of the agents. The applicability of the framework is tested through experiments in typical games selected from the literature.