The Marriage Problem with Interdependent Preferences
International Game Theory Review
This paper considers the Gale-Shapley model with interdependent preferences. Women's preferences over men are common knowledge but whether or not a man is acceptable depends on the preferences of men which are private information. It is shown that no ex-post incentive-compatible and ex-post stable matching rules exist. A characterization of ex-post incentive-compatible, ex-post individually rational and ex-post nonbossy matching rules in terms of modified priority rules is provided.
Pourpouneh, Mohsen; Ramezanian, Rasoul; and Sen, Arunava, "The Marriage Problem with Interdependent Preferences" (2020). Journal Articles. 266.