Bergantiños, Gustavo and Massó, Jordi and Neme, Alejandro
(2019):
*Individually Rational Rules for the Division Problem when the Number of Units to be Allotted is Endogenous.*

PDF
MPRA_paper_91721.pdf Download (286kB) |

## Abstract

We study individually rational rules to be used to allot, among a group of agents, a perfectly divisible good that is freely available only in whole units. A rule is individually rational if, at each preference profile, each agent finds that her allotment is at least as good as any whole unit of the good. We study and characterize two individually rational and efficient rules, whenever agents' preferences are symmetric single-peaked on the set of possible allotments. The two rules are in addition envy-free, but they differ on wether envy-freeness is considered on losses or on awards. Our main result states that (i) the constrained equal losses rule is the unique individually rational and efficient rule that satisfies justified envy-freeness on losses and (ii) the constrained equal awards rule is the unique individually rational and efficient rule that satisfies envy-freeness on awards.

Item Type: | MPRA Paper |
---|---|

Original Title: | Individually Rational Rules for the Division Problem when the Number of Units to be Allotted is Endogenous |

English Title: | Individually rational rules for the division problem when the number of units to be allotted is endogenous |

Language: | English |

Keywords: | Division problem; Single-peaked preferences; Individual rationality; Efficiency; Strategy-proofness; Envy-freeness |

Subjects: | C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory |

Item ID: | 91721 |

Depositing User: | Gustavo Bergantiño |

Date Deposited: | 08 Feb 2019 10:39 |

Last Modified: | 08 Feb 2019 10:40 |

References: | T. Adachi (2010). "The uniform rule with several commodities: a generalization of Sprumont's characterization," Journal of Mathematical Economics 46, 952--964. P. Amorós (2002). "Single-peaked preferences with several commodities," Social Choice and Welfare 19, 57--67. H. Anno and H. Sasaki (2013). "Second-best efficiency of allocation rules: strategy-proofness and single-peaked preferences with multiple commodities," Economic Theory 54, 693--716. S. Barberà, M.O. Jackson and A. Neme (1997). "Strategy-proof allotment rules," Games and Economic Behavior 18, 1--21. G. Bergantiños, J. Massó and A. Neme (2012a). "The division problem with voluntary participation," Social Choice and Welfare 38, 371--406. G. Bergantiños, J. Massó and A. Neme (2012b). "The division problem with maximal capacity constraints," SERIEs 3, 29--57. G. Bergantiños, J. Massó and A. Neme (2015). "The division problem under constraints," Games and Economic Behavior 89, 56--77. S. Ching (1992). "A simple characterization of the uniform rule," Economics Letters 40, 57--60. S. Ching (1994). "An alternative characterization of the uniform rule," Social Choice and Welfare 11, 131--136. W.J. Cho and W. Thomson (2013). "On the extension of the uniform rule to more than one commodity: existence and maximality results," mimeo. A. Erlanson and K. Flores-Szwagrzak (2015). "Strategy-proof assignment of multiple resources," Journal of Economic Theory 159, 137--162. S. Kim, G. Bergantiños and Y. Chun (2015). "The separability principle in single-peaked economies with participation constraints," Mathematical Social Sciences 78, 69--75. V. Manjunath (2012). "When too little is as good as nothing at all: rationing a disposable good among satiable people with acceptance thresholds," Games and Economic Behavior 74, 576--587. S. Morimoto, S. Serizawa and S. Ching (2013). "A characterization of the uniform rule with several commodities and agents," Social Choice and Welfare 40, 871--911. T. Sönmez (1994). "Consistency, monotonicity and the uniform rule," Economics Letters 46, 229--235. Y. Sprumont (1991). "The division problem with single-peaked preferences: a characterization of the uniform allocation rule," Econometrica 59, 509--519. W. Thomson (1994a). "Resource-monotonic solutions to the problem of fair division when preferences are single-peaked," Social Choice and Welfare 11, 205--223. W. Thomson (1994b). "Consistent solutions to the problem of fair division when preferences are single-peaked," Journal of Economic Theory 63, 219--245. W. Thomson (1995). "Population-monotonic solutions to the problem of fair division when preferences are single-peaked," Economic Theory 5, 229--246. W. Thomson (1997). "The replacement principle in private good economies with single-peaked preferences," Journal of Economic Theory 76, 145--168. W. Thomson (2010). "Fair allocation rules," in Handbook of Social Choice and Welfare, Vol. 2 (K. Arrow, A. Sen and K. Suzumura, eds.), North-Holland, Amsterdam. W. Thomson (2016). "Non-bossiness," Social Choice and Welfare 47, 665--696. |

URI: | https://mpra.ub.uni-muenchen.de/id/eprint/91721 |