Abstract
We consider Pareto-optimal matchings (POMs) in a many-to-many market of applicants and courses where applicants have preferences, which may include ties, over individual courses and lexicographic preferences over sets of courses. Since this is the most general setting examined so far in the literature, our work unifies and generalizes several known results. Specifically, we characterize POMs and introduce the Generalized Serial Dictatorship Mechanism with Ties (GSDT) that effectively handles ties via properties of network flows. We show that GSDT can generate all POMs using different priority orderings over the applicants, but it satisfies truthfulness only for certain such orderings. This shortcoming is not specific to our mechanism; we show that any mechanism generating all POMs in our setting is prone to strategic manipulation. This is in contrast to the one-to-one case (with or without ties), for which truthful mechanisms generating all POMs do exist.
This research has been co-financed by the European Union (European Social Fund - ESF) and Greek national funds under Thales grant MIS 380232 (Eirinakis, Magos, Mourtos), by grant EP/K01000X/1 from the Engineering and Physical Sciences Research Council (Manlove, Rastegari), grants VEGA 1/0344/14, 1/0142/15 from the Slovak Scientific grant agency VEGA (Cechlárová), student grant VVGS-PF-2014-463 (Oceľáková) and OTKA grant K108383 (Fleiner). The authors gratefully acknowledge the support of COST Action IC1205 Computational Social Choice.
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Cechlárová, K. et al. (2015). Pareto Optimal Matchings in Many-to-Many Markets with Ties. In: Hoefer, M. (eds) Algorithmic Game Theory. SAGT 2015. Lecture Notes in Computer Science(), vol 9347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48433-3_3
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DOI: https://doi.org/10.1007/978-3-662-48433-3_3
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