A note on the relationship between the core and stable sets in three-sided markets – was published by Ata Atay and Marina Núñez in Mathematical Social Sciences
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.
