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Duality in land rental problems

Author

Listed:
  • Valencia-Toledo, Alfredo
  • Vidal-Puga, Juan

Abstract

A single tenant demands a particular amount of land from several lessors. The way lessors rent their land can be seen as equivalent to a bankruptcy problem. We extend self-duality in bankruptcy problems to these land rental situations. We provide a complete characterization of the family of rules that satisfy self-duality. Moreover, self-duality is enough to assure that the amount of land is proportionally shared among the lessors. Adding other reasonable properties, we pick up a single rule.

Suggested Citation

  • Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2017. "Duality in land rental problems," MPRA Paper 80509, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:80509
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    File URL: https://mpra.ub.uni-muenchen.de/80509/2/MPRA_paper_80509.pdf
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    References listed on IDEAS

    as
    1. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
    2. René Brink & Youngsub Chun & Yukihiko Funaki & Boram Park, 2016. "Consistency, population solidarity, and egalitarian solutions for TU-games," Theory and Decision, Springer, vol. 81(3), pages 427-447, September.
    3. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 51-59, January.
    4. Frank Huettner, 2015. "A proportional value for cooperative games with a coalition structure," Theory and Decision, Springer, vol. 78(2), pages 273-287, February.
    5. Valencia-Toledo, Alfredo & Vidal-Puga, Juan, 2015. "Non-manipulable rules for land rental problems," MPRA Paper 67334, University Library of Munich, Germany.
    6. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    7. William Thomson, 2008. "Two families of rules for the adjudication of conflicting claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(4), pages 667-692, December.
    8. René Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, vol. 67(3), pages 303-340, September.
    9. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    10. Carmen Herrero & Antonio Villar, 2002. "Sustainability in bankruptcy problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 261-273, December.
    11. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    12. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    13. repec:spr:jogath:v:46:y:2017:i:3:d:10.1007_s00182-016-0556-4 is not listed on IDEAS
    14. van den Brink, René & Funaki, Yukihiko & van der Laan, Gerard, 2013. "Characterization of the Reverse Talmud bankruptcy rule by Exemption and Exclusion properties," European Journal of Operational Research, Elsevier, vol. 228(2), pages 413-417.
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    More about this item

    Keywords

    Self-duality; land rental problems; bankruptcy problems; proportional rule;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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