We generalise the coalition structure core to partition function games. Our definition relies only on one crucial assumption, namely that there is some internal consistency in the game: residuals of the deviation play a game similar to the initial one, and –whenever this is possible– they come to a residual core outcome. Deviating players form their optimistic or pessimistic expectations with this in mind. This leads to a recursive definition of the core. When compared to existing approaches, our core concept has a reduced sensitivity to behavioural assumptions. We look at the core of an economy with a common pool resource defined by Funaki and Yamato (1999) and find that for a number of numerical examples our core concept resolves the puzzle, which arose when more naive approaches were used. We outline possibilities for further extensions.