Studying the interaction between preference and capacity manipulation in matching markets, we prove that acyclicity is a necessary and sufficient condition that guarantees the stability of a Nash equilibrium and the strategy-proofness of truthful capacity revelation under the hospital-optimal...

This paper analyzes the role of acyclicity in singleton cores. We show that the absence of simultaneous cycles is a sufficient condition for the existence of singleton cores. Furthermore, acyclicity in the preferences of either side of the market is a minimal condition that guarantees the...

This paper presents a sequential admission mechanism where students are allowed to send multiple applications to colleges and colleges sequentially decide the applicants to enroll. The irreversibility of agents decisions and the sequential structure of the enrollments make truthful behavior a...