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A characterization of [alpha]-maximin solutions of fair division problems

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  • Sagara, Nobusumi

Abstract

This paper investigates the problem of fair division of a measurable space among a finite number of individuals and characterizes some equity concepts when preferences of each individual are represented by a nonadditive set function on a [sigma]-algebra. We show that if utility functions of individuals satisfy continuity from below and strict monotonicity, then positive Pareto optimality is equivalent to [alpha]-maximin optimality for some [alpha] in the unit simplex and Pareto-optimal [alpha]-equitability is equivalent to [alpha]-maximin optimality. These characterizations are novel in the literature.

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  • Sagara, Nobusumi, 2008. "A characterization of [alpha]-maximin solutions of fair division problems," Mathematical Social Sciences, Elsevier, vol. 55(3), pages 273-280, May.
    • Handle: RePEc:eee:matsoc:v:55:y:2008:i:3:p:273-280
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    References listed on IDEAS

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    1. Weller, Dietrich, 1985. "Fair division of a measurable space," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 5-17, February.
    2. Varian, Hal R., 1974. "Equity, envy, and efficiency," Journal of Economic Theory, Elsevier, vol. 9(1), pages 63-91, September.
    3. William Thomson, 2007. "Children Crying at Birthday Parties. Why?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 501-521, June.
    4. Mas-Colell, Andreu, 1986. "The Price Equilibrium Existence Problem in Topological Vector Lattice s," Econometrica, Econometric Society, vol. 54(5), pages 1039-1053, September.
    5. Barbanel,Julius B. Introduction by-Name:Taylor,Alan D., 2005. "The Geometry of Efficient Fair Division," Cambridge Books, Cambridge University Press, number 9780521842488, October.
    6. 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.
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    1. Farhad Hüsseinov & Nobusumi Sagara, 2013. "Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 923-940, October.

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