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Strategy-proof and Envy-free Mechanisms for House Allocation

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  • Priyanka Shende
  • Manish Purohit

Abstract

We consider the problem of allocating indivisible objects to agents when agents have strict preferences over objects. There are inherent trade-offs between competing notions of efficiency, fairness and incentives in assignment mechanisms. It is, therefore, natural to consider mechanisms that satisfy two of these three properties in their strongest notions, while trying to improve on the third dimension. In this paper, we are motivated by the following question: Is there a strategy-proof and envy-free random assignment mechanism more efficient than equal division? Our contributions in this paper are twofold. First, we further explore the incompatibility between efficiency and envy-freeness in the class of strategy-proof mechanisms. We define a new notion of efficiency that is weaker than ex-post efficiency and prove that any strategy-proof and envy-free mechanism must sacrifice efficiency even in this very weak sense. Next, we introduce a new family of mechanisms called Pairwise Exchange mechanisms and make the surprising observation that strategy-proofness is equivalent to envy-freeness within this class. We characterize the set of all neutral and strategy-proof (and hence, also envy-free) mechanisms in this family and show that they admit a very simple linear representation.

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  • Priyanka Shende & Manish Purohit, 2020. "Strategy-proof and Envy-free Mechanisms for House Allocation," Papers 2010.16384, arXiv.org.
    • Handle: RePEc:arx:papers:2010.16384
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    References listed on IDEAS

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    Cited by:

    1. Basteck, Christian & Ehlers, Lars, 2021. "Strategy-Proof and Envy-Free Random Assignment," Rationality and Competition Discussion Paper Series 307, CRC TRR 190 Rationality and Competition.
    2. Basteck, Christian & Ehlers, Lars H., 2022. "Strategy-proof and envy-free random assignment," Discussion Papers, Research Unit: Market Behavior SP II 2022-208, WZB Berlin Social Science Center.
    3. Basteck, Christian & Ehlers, Lars H., 2023. "On the constrained efficiency of strategy-proof random assignment," Discussion Papers, Research Unit: Market Behavior SP II 2023-202, WZB Berlin Social Science Center.

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