# 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. 1.

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

2. 2.

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

3. 3.

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

4. 4.

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

5. 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. 6.

We thank an anonymous referee for suggesting this alternative application.

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## Author information

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 (2019) doi:10.1007/s00182-019-00684-2