An Axiom-Based Comparison of the Core and Other Core Extensions

We propose an axiomatic framework that allows a unified analysis of the core and three other related cooperative solution concepts that are applicable even when the core itself is empty. Existing axiomatizations of the core and similar concepts of a cooperative game include the desired form of feasibility (or efficiency) 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. Our characterization of the core can be adapted to axiomatize extensions of the core concept that generate predictions for games with empty cores. We use this avenue to provide new axiomatizations of the aspiration set, the aspiration core, and the c-core.