The Core in the Presence of Externalities

Abstract

We generalise the coalition structure core to partition function games. Our definition relies only on a single 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. Compared to existing approaches, our core concept displays a reduced sensitivity to behavioural assumptions. We consider the core of an economy with a common pool resource defined by Funaki and Yamato [4], and show that for a number of numerical examples our core concept resolves the puzzle arising when more naive approaches were used. We outline possibilities for further extensions.