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The Hospitals / Residents problem with Couples (HRC) is a generalisation of the classical Hospitals / Resident problem (HR) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of (typically geographically close) hospitals. In this paper we give a new NP-completeness result for the problem of deciding whether a stable matching exists, in highly restricted instances of HRC. Further, we present an Integer Programming (IP)...
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Scarf’s algorithm [18] provides fractional core elements for NTU-games. Biró and Fleiner [3] showed that Scarf’s algorithm can be extended for capacitated NTU-games. In this setting agents can be involved in more than one coalition at a time, cooperations may be performed with different intensities up to some limits, and the contribution of the agents can also differ in a coalition. The fractional stable solutions for the above model, produced by the extended Scarf algorithm, are called...
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To assign teachers to schools, a modified version of the well-known deferred acceptance mechanism has been proposed in the literature and is used in practice. We show that this mechanism fails to be fair and efficient for both teachers and schools. We identify a class of strategyproof mechanisms that cannot be improved upon in terms of both efficiency and fairness. Using a rich dataset on teachers’ applications in France, we estimate teachers preferences and perform a counterfactual analysis....
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