The Dutta-Ray solution and the Shapley value are two well-known examples of population-monotonic solutions on the domain of convex games. We provide a new formula for the Dutta-Ray solution from which population-monotonicity immediately follows. Then we define a new family of...

We show that the nucleolus is not aggregate-monotonic on the domain of convex games, and that this lack of monotonicity holds even if there are as few as four agents.

On the domain of convex games, many desirable properties of solutions are compatible and there are many single-valued solutions that are intuitively appealing. We establish some interesting logical relations among properties of single-valued solutions. In particular, we introduce a new property,...