Consistency implies equal treatment in TU-games

Many solutions for TU-games coincide with the “standard solution” for the two-agent case. We study its weighted generalizations. In particular, we study whether max consistency is compatible with “2-weighted-standardness.” We show that on the domain of all TU-games, efficiency, 2-weighted-standardness, and max consistency jointly imply equal treatment of equals. It follows from this result that on the same domain, the prenucleolus is the only single-valued solution satisfying efficiency, 2-weighted-standardness, zero-independence, and max consistency. This uniqueness result does not hold on the domain of convex games. We define the family of “sequential nucleoli” on this domain, and show that this family of solutions is characterized by efficiency, 2-weighted-standardness, and max consistency.