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Reallocation with priorities and minimal envy mechanisms

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Abstract

We investigate the problem of reallocation with priorities where one has to assign objects or positions to individuals. Agents can have an initial ownership over an object. Each object has a priority ordering over the agents. In this framework, there is no mechanism that is both individually rational (IR) and stable, i.e. has no blocking pairs. Given this impossibility, an alternative approach is to compare mechanisms based on the blocking pairs they generate. A mechanism has minimal envy within a set of mechanisms if there is no other mechanism in the set that always leads to a set of blocking pairs included in the one of the former mechanism. Our main result shows that the modified Deferred Acceptance mechanism (Guillen and Kesten in Int Econ Rev 53(3):1027–1046, 2012), is a minimal envy mechanism in the set of IR and strategy-proof mechanisms. We also show that an extension of the Top Trading Cycle (Karakaya et al. in J Econ Theory 184:104948, 2019) mechanism is a minimal envy mechanism in the set of IR, strategy-proof and Pareto-efficient mechanisms. These two results extend the existing ones in school choice.

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  1. Ecole polytechnique, CREST and Institut Polytechnique de Paris, Palaiseau, France

    Julien Combe

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  1. Julien Combe
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Correspondence to Julien Combe.

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I am grateful to Elias Bouacida, Yeon-Koo Che, Simon Gleyze, Philippe Jehiel, Josuè Ortega, Vasiliki Skreta, Olivier Tercieux and seminar participants at UCL. I am also grateful for the support from Vasiliki Skreta’s ERC Grant No. 682417, Frontiers in Design—Frontiers in Mechanism Design: Methodology and Applications. All potential mistakes are mine.

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Combe, J. Reallocation with priorities and minimal envy mechanisms. Econ Theory 76, 551–584 (2023). https://doi.org/10.1007/s00199-022-01465-x

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