Abstract
Characterizations of the classes of all choice functions that select the cores or the externally stable cores induced by an underlying revealed dominance digraph are provided. Relying on such characterizations, the basic order-theoretic structure of the corresponding sets of revealed cores is also analyzed. In particular, it is shown that the poset of all revealed cores ordered by set inclusion is a median meet semilattice: therefore, any profile of revealed cores may be aggregated by means of the simple majority rule.
Highlights
The core of a game is the set of its undominated outcomes, with respect to a suitably defined dominance irreflexive relation, or loopless digraph
The paper is organized as follows: Section 2 includes a presentation of the model and the main characterization results; Section 3 provides some basic results concerning the order-theoretic properties of the classes of revealed core-solutions previously characterized; Section 4 consists of a few concluding remarks
Choice functions with full domain which may be regarded as core-solutions or externally stable core solutions of an underlying dominance digraph ( X, ∆) have been characterized both in the general case and for asymmetric dominance digraphs
Summary
The core of a game is the set of its undominated outcomes, with respect to a suitably defined dominance irreflexive relation, or loopless digraph. The present paper is aimed at filling this gap in the literature by addressing the general core revelation problem with full domain as formulated above. It contributes to the extant literature in the following ways: it provides characterizations of all choice functions with full domain—proper or not—that represent revealed cores, under several variants of the notion of core (Theorems 7, 10, and 14). The paper is organized as follows: Section 2 includes a presentation of the model and the main characterization results; Section 3 provides some basic results concerning the order-theoretic properties of the classes of revealed core-solutions previously characterized; Section 4 consists of a few concluding remarks
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