- Autor
- Dall'Aglio Marco (LUISS University, Italy), Di Luca Camilla (LUISS University, Italy), Milone Lucia (LUISS University, Italy)
- Tytuł
- Finding the Pareto Optimal Equitable Allocation of Homogeneous Divisible Goods Among Three Players
- Źródło
- Operations Research and Decisions, 2017, vol. 27, no. 3, s. 35-50, rys., bibliogr. 16 poz.
- Słowa kluczowe
- Optimum Pareto, Teoria grafów, Algorytmy
Pareto optimality, Graph theory, Algorithms - Uwagi
- summ.
- Abstrakt
- 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)
- Dostępne w
- Biblioteka Główna Uniwersytetu Ekonomicznego w Krakowie
Biblioteka SGH im. Profesora Andrzeja Grodka
Biblioteka Główna Uniwersytetu Ekonomicznego w Katowicach
Biblioteka Główna Uniwersytetu Ekonomicznego w Poznaniu - Pełny tekst
- Pokaż
- Bibliografia
-
- BARBANEL J.B., On the structure of Pareto optimal cake partitions, J. Math. Econ., 2000, 33 (4), 401-424.
- BARBANEL J.B., The Geometry of Efficient Fair Division, Cambridge University Press, Cambridge 2005.
- 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.
- BOGOMOLNAIA A., MOULIN H., Competitive fair division under linear preferences, Working Papers 2016-07, Business School, Economics, University of Glasgow.
- BOGOMOLNAIA A., MOULIN H., SANDOMIRSKIY F., YANOVSKAYA E., Competitive division of a mixed manna, Econometrica, 2017, accepted for publication.
- 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.
- BRAMS S.J., TAYLOR A.D., Fair Division. From Cake-Cutting to Dispute Resolution, Cambridge University Press, Cambridge 1996.
- BRAMS S.J., TAYLOR A.D., The Win-Win Solution. Guaranteeing Fair Shares to Everybody, W.W. Norton, New York 1999.
- DALL'AGLIO M., The Dubins-Spanier optimization problem in fair division theory, J. Comp. Appl. Math., 2001, 130 (1), 17-40.
- 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.
- DALL'AGLIO M., HILL T.P., Maximin share and minimax envy in fair-division problems, J. Math. Anal. Appl., 2003, 281, 346-361.
- DEMKO S., HILL T.P., Equitable distribution of indivisible objects, Math. Soc. Sci., 1988, 16 (2), 145-158.
- KALAI E., Proportional solutions to bargaining situations. Interpersonal utility comparisons, Econometrica, 1977, 45 (7), 1623-1630.
- KALAI E., SMORODINSKY M., Other solutions to Nash's bargaining problem, Econometrica, 1975, 43 (3), 513-518.
- OLVERA-LÓPEZ W., SÁNCHEZ- SÁNCHEZ F., An algorithm based on graphs for solving a fair division problem, Oper. Res., 2014, 14 (1), 11-27.
- WELLER D., Fair division of a measurable space, J. Math. Econ., 1985, 14 (1), 5-17.
- Cytowane przez
- ISSN
- 2081-8858
- Język
- eng
- URI / DOI
- http://dx.doi.org/10.5277/ord170303
