We present some mathematical theorems which are used to generalize previous results on the existence of maximal elements and of equilibrium.Our main theorem in this paper is a new existence proof for an equilibrium in an abstract economy, which is closely related to a previous result of Borglin-Keiding, and Shafer-Sonneschein, but allows for an i&nite number of commodities and a countably infinite number of agents.

We introduce a new core concept for an exchange economy with differential information which is contained in the coarse core concept of Wilson (1978). We prove the existence of (i) a core allocation for an exchange economy with differential information and (ii) an a-core strategy for a game in normal form with differential information.

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: We analyse the coarse, the fine, and the private information core allocation of an exchange economy with differential information. The basic questions that we address are whether the above concepts are: (i) coalitionally incentive compatible, i.e., does truthful revelation of information in each coalition occur; and (ii) take into account the information superiority or information advantage of an agent. Moreover, the above three concepts are examined in the presence of externalities and a comparison and interpretation of all of these core notions is provided.We wish to thank Stefan Krasa and Anne Villamil for several useful suggestions. Obviously we are responsible for all errors.