Match Stability with a Costly and Flexible Number of Positions

One of the main goals of two-sided matching mechanisms is to pair two groups of agents in a stable manner. Stability means that no pair of agents has an incentive to deviate from their assigned match. The outcome of such a match can have significant consequences for the participants involved. Most existing research in this field assumes that the quotas of organizations are fixed and externally determined, which may not always be realistic. We introduce the concept of slot stability, which considers the possibility that organizations may want to adjust their quotas after the match process. To address this issue, we propose an algorithm that generates both stable and slot-stable matches by using flexible, endogenous quotas.