A note on the relationship between the core and stable sets in three-sided markets

Abstract

We analyze the extent to which two known results of the relationship between the core and the stable sets for two-sided assignment games can be extended to three-sided assignment games. We find that the dominant diagonal property is necessary for the core to be a stable set and, likewise, sufficient when each sector of the three-sided market has two agents. Unlike the two-sided case, the union of the extended cores of all the -compatible subgames with respect to an optimal matching may not be a von Neumann-Morgenstern stable set.