When does the cumulative offer process produce an allocation?

Official URL: http://risc01.sabanciuniv.edu/record=b1819798 (Table of Contents)

This thesis examines the properties of an algorithm, namely the Cumulative Offer Process (COP), which has been the principal algorithm in the matching with contracts setting. Matching with contracts is an allocation problem which employs contracts as its basic unit of analysis. We examine properties of COP under the substitutes (S) condition as well as the bilateral substitutes (BS) and the unilateral substitutes (US) conditions. These conditions are imposed on the choice functions of hospitals to obtain desirable matchings. In our research, we found that in the absence of IRC, the US, and hence automatically the BS, does not guarantee the existence of a feasible allocation that is produced by COP, yet S guarantees it. Therefore, our study shows that IRC is an essential property of choice functions of hospitals in order for the COP algorithm to be well-defined under BS or US.