The SD-prekernel for TU games

We introduce and analyze a new solution concept for TU games:The Surplus Distributor Prekernel. Like the prekermel, the new solu- tion is based on the an alternative motion of complaint of one player against other with respect to an allocation. The SD-prekernel contains the SD-prenucleolus and they coincide in the class of convex games. This result allows us to prove that in bankruptcy problems the SD-prekernel and the Minimal Overlapping rule select the same allocation.

A monotonic core concept for convex games: The SD-prenucleolus

We prove that the SD-prenucleolus satisfies monotonicity in the class of convex games. The SD-prenucleolus is thus the only known continuous core concept that satisfies monotonicity for convex games. We also prove that for convex games the SD-prenucleolus and the SD-prekernel coincide.