Monotonic core solutions: Beyond Young's theorem

We introduce two new monotonicity properties for core concepts: single-valued solution concepts that always select a core allocation whenever the game is balanced (has a nonempty core). We present one result of impossibility for one of the properties and we pose several open questions for the second property. The open questions arise because the most important core concepts (the nucleolus and the per capita nucleolus) do not satisfy the property even in the class of convex games.