The Projective Core of Symmetric Games with Externalities

The purpose of this paper is to analyze stable distributions and coalition structures in certain economic situations. We consider the projective core as the most myopic core of the cores defined for games with externalities. Although the core is often defined only for the grand coalition, we define the projective core for each coalition structure and apply it to some economic models such as the public goods game, the Cournot oligopoly, and the common pool resource game. Moreover, we formulate the Bertrand oligopoly as a game with externalities. We argue that symmetry is a common property of these models in terms of the partition function. We offer some general results that hold for all symmetric games with externalities and discuss the implications of the economic models. We also provide necessary and sufficient conditions for the projective core of the models to be nonempty.