We propose a new version of ATLP (“ATL with plausibility”), a logic for reasoning about the outcome of rational play in game-like scenarios. Unlike in [8], where two different extensions of ATL were used for specifying rationality and reasoning about agents’ behavior, we now propose that rationality specifications can be written in ATLP itself, and nested in ATLP formulae. We believe that the new version is more elegant, and also more flexible and expressive. Finally, we present some ATLP characterizations of solution concepts and discuss the notion of qualitative solution concept, based on winning conditions defined by temporal path formulae.