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Reassignment-proof rules for land rental problems

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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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