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Finding Maxmin Allocations in Cooperative and Competitive Fair Division

Author

Listed:
  • Marco Dall'Aglio

    (LUISS University Rome, Italy)

  • Camilla Di Luca

    ("G. D'Annunzio" University Pescara, Italy)

Abstract

We consider upper and lower bounds for maxmin allocations of a completely divisible good in both competitive and cooperative strategic contexts. We then derive a subgradient algorithm to compute the exact value up to any fixed degree of precision.

Suggested Citation

  • Marco Dall'Aglio & Camilla Di Luca, 2011. "Finding Maxmin Allocations in Cooperative and Competitive Fair Division," Working Papers 2011.88, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2011.88
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    References listed on IDEAS

    as
    1. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    2. Barbanel, Julius, 1999. "Partition ratios, Pareto optimal cake division, and related notions," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 401-428, December.
    3. Legut, Jerzy, 1990. "On totally balanced games arising from cooperation in fair division," Games and Economic Behavior, Elsevier, vol. 2(1), pages 47-60, March.
    4. Brams,Steven J. & Taylor,Alan D., 1996. "Fair Division," Cambridge Books, Cambridge University Press, number 9780521556446.
    5. Legut, J. & Potters, J.A.M. & Tijs, S.H., 1994. "Economies with land : A game theoretical approach," Other publications TiSEM 37ff121d-d79c-4e41-a06a-9, Tilburg University, School of Economics and Management.
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    More about this item

    Keywords

    Fair Division; Maxmin Allocation; Kalai Bargaining Solution; Cooperative Game Theory;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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