PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2017 | 27 | nr 3 | 35--50
Tytuł artykułu

Finding the Pareto Optimal Equitable Allocation of Homogeneous Divisible Goods Among Three Players

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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. (original abstract)
Rocznik
Tom
27
Numer
Strony
35--50
Opis fizyczny
Twórcy
  • LUISS University, Italy
  • LUISS University, Italy
autor
  • LUISS University, Italy
Bibliografia
  • [1] BARBANEL J.B., On the structure of Pareto optimal cake partitions, J. Math. Econ., 2000, 33 (4), 401-424.
  • [2] BARBANEL J.B., The Geometry of Efficient Fair Division, Cambridge University Press, Cambridge 2005.
  • [3] BARBANEL J.B., ZWICKER W.S., Two applications of a theorem of Dvoretzky, Wald, and Wolfovitz to cake division, Theory Dec., 1997, 43 (2), 203-207.
  • [4] BOGOMOLNAIA A., MOULIN H., Competitive fair division under linear preferences, Working Papers 2016-07, Business School, Economics, University of Glasgow.
  • [5] BOGOMOLNAIA A., MOULIN H., SANDOMIRSKIY F., YANOVSKAYA E., Competitive division of a mixed manna, Econometrica, 2017, accepted for publication.
  • [6] BRAMS S.J., JONES M.A., KLAMLER C., N-person cake-cutting: There may be no perfect division, Am. Math. Monthly, 2013, 120 (1), 35-47.
  • [7] BRAMS S.J., TAYLOR A.D., Fair Division. From Cake-Cutting to Dispute Resolution, Cambridge University Press, Cambridge 1996.
  • [8] BRAMS S.J., TAYLOR A.D., The Win-Win Solution. Guaranteeing Fair Shares to Everybody, W.W. Norton, New York 1999.
  • [9] DALL'AGLIO M., The Dubins-Spanier optimization problem in fair division theory, J. Comp. Appl. Math., 2001, 130 (1), 17-40.
  • [10] DALL'AGLIO M., DI LUCA C., MILONE L., Characterizing and Finding the Pareto Optimal Equitable Allocation of Homogeneous Divisible Goods Among Three Players, arXiv:1606.01028, 2016.
  • [11] DALL'AGLIO M., HILL T.P., Maximin share and minimax envy in fair-division problems, J. Math. Anal. Appl., 2003, 281, 346-361.
  • [12] DEMKO S., HILL T.P., Equitable distribution of indivisible objects, Math. Soc. Sci., 1988, 16 (2), 145-158.
  • [13] KALAI E., Proportional solutions to bargaining situations. Interpersonal utility comparisons, Econometrica, 1977, 45 (7), 1623-1630.
  • [14] KALAI E., SMORODINSKY M., Other solutions to Nash's bargaining problem, Econometrica, 1975, 43 (3), 513-518.
  • [15] OLVERA-LÓPEZ W., SÁNCHEZ- SÁNCHEZ F., An algorithm based on graphs for solving a fair division problem, Oper. Res., 2014, 14 (1), 11-27.
  • [16] WELLER D., Fair division of a measurable space, J. Math. Econ., 1985, 14 (1), 5-17.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171491018

Zgłoszenie zostało wysłane

Zgłoszenie zostało wysłane

Musisz być zalogowany aby pisać komentarze.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.