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A note on the relationship between the core and stable sets in three-sided markets
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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.
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ATAY, Ata and NÚÑEZ, Marina (Núñez Oliva). A note on the relationship between the core and stable sets in three-sided markets. Mathematical Social Sciences. 2019. Vol. 98, num. March, pags. 10-14. ISSN 0165-4896. [consulted: 30 of October of 2026]. Available at: https://hdl.handle.net/2445/150700