Maximizing selections from the core of a cooperative game

A core selection is a function which for each cooperative game with non‐empty core selects a subset, possibly a single element, of the core. In this paper, we study selections which maximize some function or binary relation on the core. We present an axiomatic characterization of such core selections, as well as a local characterization using duality which can be applied to investigate properties of core selections. We give an application of the local characterization to a question of coalitional monotonicity of core selections.