Many-to-one matching markets with externalities among firms

We study a labor market described by a many-to-one matching market with externalities among firms in which each firm’s preferences depend not only on workers whom it hires, but also on workers whom its rival firms hire. We define a new stability concept called weak stability and investigate its existence problem. We show that when the preferences of firms satisfy an extension of substitutability and two new conditions called increasing choice and no external effect by an unchosen worker, then a weakly stable matching exists. We also show that a weakly stable matching may fail to exist without these restrictions.     

A modified deferred acceptance algorithm for conditionally lexicographic-substitutable preferences

We study a class of preferences that generalize substitutable ones and allows complementarities in a college admissions model. We show that a stable matching exists under this class of preferences by using an algorithm which we call the Conditional Deferred Acceptance Algorithm. Furthermore, we show that the algorithm is strategy-proof for the student side if we assume in addition a law of aggregate demand adapted to our setting.