On the importance of reduced games in axiomatizing core extensions

We propose new axiomatizations of the core and three related solution concepts that also provide predictions for (classes of) games in which the core itself is empty. Our results showcase the importance of the reduced game formulation and identify the corresponding converse consistency property as the differentiating characteristic between the core and its various extensions. Existing axiomatizations of the core and similar concepts include the required form of feasibility in the generic definition of a solution concept and/or are restricted to the domain of games for which existence is guaranteed. We dispense of both practices, thus opening up the possibility of comparing, via basic axioms, solution concepts that have different feasibility constraints and domains.