The aggregate-monotonic core

We introduce the aggregate-monotonic core as the set of allocations of a transferable utility cooperative game attainable by single-valued solutions that satisfy core-selection and aggregate-monotonicity. We provide a necessary and sufficient condition for the coincidence of the core and the aggregate-monotonic core. Finally, we introduce upper and lower aggregate-monotonicity for set-valued solutions, and characterize the aggregate-monotonic core using core-selection and upper and lower aggregate-monotonicity.