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Disputed lands

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  • Dall'Aglio, Marco
  • Maccheroni, Fabio

Abstract

In this paper we consider the classical problem of dividing a land among many agents so that everybody is satisfied with the parcel she receives. In the literature, it is usually assumed that all the agents are endowed with cardinally comparable, additive, and monotone utility functions. In many economic and political situations violations of these assumptions may arise. We show how a family of cardinally comparable utility functions can be obtained starting directly from the agents' preferences, and how a fair division of the land is feasible, without additivity or monotonicity requirements. Moreover, if the land to be divided can be modeled as a finite dimensional simplex, it is possible to obtain envy free (and a fortiori fair) divisions of it into subsimplexes. The main tool is an extension of a representation theorem of Gilboa and Schmeidler [Gilboa, I., Schmeidler, D., 1989, Maxmin expected utility with non-unique prior. J. Math. Econ. 18, 141-153].

Suggested Citation

  • Dall'Aglio, Marco & Maccheroni, Fabio, 2009. "Disputed lands," Games and Economic Behavior, Elsevier, vol. 66(1), pages 57-77, May.
    • Handle: RePEc:eee:gamebe:v:66:y:2009:i:1:p:57-77
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    References listed on IDEAS

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    1. Berliant, Marcus & Thomson, William & Dunz, Karl, 1992. "On the fair division of a heterogeneous commodity," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 201-216.
    2. Ichiishi, Tatsuro & Idzik, Adam, 1999. "Equitable allocation of divisible goods," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 389-400, December.
    3. Berliant, Marcus & Dunz, Karl, 2004. "A foundation of location theory: existence of equilibrium, the welfare theorems, and core," Journal of Mathematical Economics, Elsevier, vol. 40(5), pages 593-618, August.
    4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    5. Itzhak Gilboa, 2004. "Uncertainty in Economic Theory," Post-Print hal-00756317, HAL.
    6. Fabio Maccheroni & Fabio Maccheroni & Massimo Marinacci & Massimo Marinacci, 2003. "How to cut a pizza fairly: Fair division with decreasing marginal evaluations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 457-465, June.
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    Cited by:

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    2. Erel Segal-Halevi & Shmuel Nitzan, 2014. "Cake Cutting – Fair and Square," Working Papers 2014-01, Bar-Ilan University, Department of Economics.
    3. Segal-Halevi, Erel & Nitzan, Shmuel & Hassidim, Avinatan & Aumann, Yonatan, 2017. "Fair and square: Cake-cutting in two dimensions," Journal of Mathematical Economics, Elsevier, vol. 70(C), pages 1-28.

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    More about this item

    Keywords

    Fair division Envy Preference representation;

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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