The absence of simultaneous cycles is a sufficient condition for the existence of singleton cores. Acyclicity in the preferences of either side of the market is a minimal condition that guarantees the existence of singleton cores

Studying the interactions 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...

Sasaki and Toda (1996) claim that, in marriage markets with externalities, the stable set and the core are not equal, differently to what happen in marriage markets without externalities. However, the example that proves this claim has an error. By proposing an alternative example we prove that...