UC Berkeley

I study the stability and doctor-optimality of doctors' proposing cumulative offer process in the many-to-one matching with contracts. First, I explore some conventional hospital-by-hospital conditions on each hospital's choice function, and show that unilateral substitutability is equivalent to observable substitutability across doctors combined with cumulative offer achievability, each of which is a necessary condition for cumulative offer process to be doctor-optimally stable in a sense that if a hospital does not satisfy the condition, then we could construct some choice functions for other hospitals such that cumulative offer process is not doctor-optimally stable for some doctors' preference profile. Then, I focus on the joint properties of the choice functions for the entire group of hospitals and introduce two joint conditions---independence of proposing order and group cumulative offer achievability---and show that when these conditions are satisfied, cumulative offer process is always doctor-optimally stable. And it is by far the weakest sufficient condition. Moreover, these two conditions are necessary in a sense that if not, then there exists a doctors' preference profile and a proposing order such that cumulative offer process is not doctor-optimally stable. At last, I also introduce doctor's preference monotonicity and show that when cumulative offer process is doctor-optimally stable, this condition guarantees its strategy-proofness.