We propose an extension of alternating-time temporal logic, that can be used for reasoning about the behavior and abilities of agents under various rationality assumptions. Categories and Subject Descriptors I.2.11 [Artificial Intelligence]: Distributed Artificial Intelligence— Multiagent Systems; I.2.4 [Artificial Intelligence]: Knowledge Representation Formalisms and Methods—Modal logic General Terms Theory Keywords multi-agent systems, game theory, temporal logic, rationality