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Reclaim-proof allocation of indivisible objects |
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| Affiliation: | 1. Deakin University, Australia;2. North Carolina State University, United States of America;3. Center for Behavioral Institutional Design, NYU Abu Dhabi, United Arab Emirates;1. School of Mathematical Sciences, Tel-Aviv University, Israel;2. School of International Trade and Economics, University of International Business and Economics, China;1. Department of Economics, University of Padova, via del Santo 33, 35123 Padova, Italy;2. School of Social Sciences, The University of Manchester, Manchester M13 9PL, United Kingdom;3. Economics and Planning Unit, Indian Statistical Institute, 7 S.J.S Sansanwal Marg, New Delhi-110016, India;4. Umeå University, Umeå, Sweden |
| Abstract: | We study desirability axioms imposed on allocations in indivisible object allocation problems. The existing axioms in the literature are various conditions of robustness to blocking coalitions with respect to agentsʼ ex ante (individual rationality and group rationality) and ex post (Pareto efficiency) endowments. We introduce a stringent axiom that encompasses and strengthens the existing ones. An allocation is reclaim-proof if it is robust to blocking coalitions with respect to any conceivable interim endowments of agents. This is an appealing property in dynamic settings, where the assignments prescribed by an allocation to be implemented need to be made in multiple rounds rather than all in one shot. We show that an allocation is reclaim-proof if and only if it is induced by a YRMH–IGYT mechanism (introduced by Abdulkadiroğlu and Sönmez, 1999) and if and only if it is a competitive allocation. |
| Keywords: | Indivisible object allocation House allocation with existing tenants House allocation Housing market Reclaim-proof Competitive allocation Core |
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