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Finding the Pareto optimal equitable allocation of homogeneous divisible goods among three players

Author

Listed:
  • Marco Dall'Aglio
  • Camilla Di Luca
  • Lucia Milone
Abstract
We consider the allocation of a finite number of homogeneous divisible items among three players. Under the assumption that each player assigns a positive value to every item, we develop a simple algorithm that returns a Pareto optimal and equitable allocation. This is based on the tight relationship between two geometric objects of fair division: The Individual Pieces Set (IPS) and the Radon–Nykodim Set (RNS). The algorithm can be considered as an extension of the Adjusted Winner procedure by Brams and Taylor to the three-player case, without the guarantee of envy-freeness.

Suggested Citation

  • Marco Dall'Aglio & Camilla Di Luca & Lucia Milone, 2017. "Finding the Pareto optimal equitable allocation of homogeneous divisible goods among three players," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(3), pages 35-50.
    • Handle: RePEc:wut:journl:v:3:y:2017:p:35-50:id:1330
    DOI: 10.5277/ord170303
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    References listed on IDEAS

    as
    1. Anna Bogomolnaia & Herve Moulin, 2016. "Competitive Fair Division under linear preferences," Working Papers 2016_07, Business School - Economics, University of Glasgow.
    2. Anna Bogomolnaia & Hervé Moulin & Fedor Sandomirskiy & Elena Yanovskaya, 2017. "Competitive Division of a Mixed Manna," Econometrica, Econometric Society, vol. 85(6), pages 1847-1871, November.
    3. Demko, Stephen & Hill, Theodore P., 1988. "Equitable distribution of indivisible objects," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 145-158, October.
    4. Julius Barbanel & William Zwicker, 1997. "Two applications of a theorem of Dvoretsky, Wald, and Wolfovitz to cake division," Theory and Decision, Springer, vol. 43(2), pages 203-207, September.
    5. Kalai, Ehud & Smorodinsky, Meir, 1975. "Other Solutions to Nash's Bargaining Problem," Econometrica, Econometric Society, vol. 43(3), pages 513-518, May.
    6. Barbanel, Julius, 2000. "On the structure of Pareto optimal cake partitions," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 401-424, May.
    7. Kalai, Ehud, 1977. "Proportional Solutions to Bargaining Situations: Interpersonal Utility Comparisons," Econometrica, Econometric Society, vol. 45(7), pages 1623-1630, October.
    8. Barbanel,Julius B. Introduction by-Name:Taylor,Alan D., 2005. "The Geometry of Efficient Fair Division," Cambridge Books, Cambridge University Press, number 9780521842488, September.
    9. Brams, Steven J. & Jones, Michael A. & Klamler, Christian, 2011. "N-Person cake-cutting: there may be no perfect division," MPRA Paper 34264, University Library of Munich, Germany.
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