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Reassignment-proof rules for land rental problems

International Journal of Game Theory volume 49, pages 173–193 (2020)Cite this article

Abstract

We consider land rental problems where there are several communities that can act as lessors and a single tenant who does not necessary need all the available land. A rule should determine which communities become lessors, how much land they rent and at which price. We present a complete characterization of the family of rules that satisfy reassignment-proofness by merging and spliting, apart from land monotonicity. We also define two parametric subfamilies. The first one is characterized by adding a property of weighted standard for two-person. The second one is characterized by adding consistency and continuity.

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Notes

  1. We use the terms c and E because of their resemblance to bankruptcy problems.

  2. Since rc(N) is constant, this condition is equivalent to \(\mu (E)-rE\) be maximum.

  3. This condition holds, for example, when \(\mu \) is increasing, strictly concave, and \(\mu (0) \le 0\).

  4. In fact, RLM applied to problems with a single lessor would also suffice.

  5. For example, \(x_i = \frac{c_iE}{c(N)}\) for all \(i\in N\) when \(r \le \frac{K}{2E}\), and \(x_i = \min \{c_i, \lambda \}\) for all \(i\in N\), where \(\lambda \) solves \(\sum _{i\in N}\min \{c_i, \lambda \} = E\), when \(r > \frac{K}{2E}\).

  6. We thank an anonymous referee for suggesting this alternative application.

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Authors and Affiliations

  1. Departamento de Matemáticas y Estadística, Universidad Nacional de San Antonio Abad del Cusco, Cusco, Peru

    Alfredo Valencia-Toledo

  2. ECOSOT-ECOBAS and Departamento de Estatística e IO, Universidade de Vigo, Vigo, Spain

    Juan Vidal-Puga

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  1. Alfredo Valencia-Toledo
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Correspondence to Alfredo Valencia-Toledo.

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Alfredo Valencia-Toledo thanks the Ministry of Education of Peru for its financial support through the “Beca Presidente de la República” grant of the “Programa Nacional de Becas y Crédito Educativo (PRONABEC)”. Juan Vidal-Puga acknowledges financial support from the Spanish Ministerio de Economía y Competitividad through Grant ECO2014-52616-R., Ministerio de Economía, Industria y Competitividad through Grant ECO2017-82241-R, and Xunta de Galicia (GRC 2015/014).

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Valencia-Toledo, A., Vidal-Puga, J. Reassignment-proof rules for land rental problems. Int J Game Theory 49, 173–193 (2020). https://doi.org/10.1007/s00182-019-00684-2

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