On the domain of two-sided assignment markets with agents' reservation values, the nucleolus is axiomatized as the unique solution that satisfies consistency with respect to Owen's reduced game and symmetry of maximum complaints of the two sides. As an adjunt, we obtain a geometric characterization of the nucleolus by means of a strong form of the bisection property that characterizes the intersection between the core and the kernel of a coalitional game in Maschler et al. (1979).
The existence of von Neumann-Morgenstern solutions (stable sets) for assignment games has been an unsolved question since Shapley and Shubik [11].For each optimal matching between buyers and sellers, Shubik [12] proposed considering the union of the core of the game and the core of the subgames that are compatible with this matching. We prove in the present paper that this set is the unique stable set for the assignment game that excludes thirdparty payments with respect to a fixed optimal matching. Moreover, the stable sets that we characterize, as well as any other stable set of the assignment game, have a lattice structure with respect to the same partial order usually defined on the core.
The main objective of the paper is to study the locus of all core selection and aggregate monotonic point solutions of a TU-game: the aggregate-monotonic core. Furthermore, we characterize the class of games for which the core and the aggregate-monotonic core coincide. Finally, we introduce a new family of rules for TU-games which satisfy core selection and aggregate monotonicity.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.