Binary operations and lattice structure for a model of matching with contracts |
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| Institution: | 1. The Korea University, Rm523, Woodang Hall, 145 Anam-ro, Seongbuk-gu, Seoul, 136-701, South Korea;2. The University of Exeter, Streatham Court, Rennes Drive, Exeter, EX4 4PU, UK;1. Institute of Modern Optics and MOE Key Laboratory of Optical Information Science & Technology, Nankai University, Tianjin 300071, PR China;2. College of Pharmacy, Nankai University, Tianjin 300071, PR China;3. College of Chemistry, Nankai University, Tianjin 300071, PR China;1. Fujian Key Laboratory of Sensing and Computing for Smart City, School of Information Science and Engineering, Xiamen University, Fujian 361005, China;2. School of Computer and Information Engineering, Xiamen University of Technology, Fujian 361024, China;3. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China;4. Biometrics Research Centre, The Hong Kong Polytechnic University, Hong Kong;1. Université de Franche-Comté, CRESE, 30 Avenue de l’Observatoire, 25009 Besançon, France;2. Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne and IXXI, France;3. Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France |
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| Abstract: | We consider a restricted model of many-to-one matching with contracts and we order the set of stable allocations according both to the unanimous-for-doctors partial ordering and Blair’s partial ordering for hospitals. We define two binary operations to calculate the least upper bound and greatest lower bound for each pair of elements of this set in a simple way. By using these operations, we show that the set of stable allocations has dual lattice structures, thus reflecting an expected counterposition of interests between both sides of the market. |
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