On the fair division of a heterogeneous commodity☆
References (23)
An equilibrium existence result for an economy with land
Journal of Mathematical Economics
(1985)- et al.
A foundation of location theory: Consumer preferences and demand
Journal of Economic Theory
(1988) Existence of equilibria in economies with infinitely many commodities
Journal of Economic Theory
(1972)On the core of a land trading game
Regional Science and Urban Economics
(1991)Equity, envy, and efficiency
Journal of Economic Theory
(1974)Fair division of a measurable space
Journal of Mathematical Economics
(1985)Dividing a cake fairly
Journal of Mathematical Analysis and Applications
(1980)- (1964)
- et al.
A foundation of location theory: Existence of equilibrium, the welfare theorems, and core
(1989) Drei Satze über die n-dimensionale euklidische Sphäre
Fundamentals of Mathematics
(1933)
How to cut a cake fairly
American Mathematical Monthly
Cited by (81)
Fair division of indivisible goods: Recent progress and open questions
2023, Artificial IntelligenceKeep your distance: Land division with separation
2023, Computational Geometry: Theory and ApplicationsAlmost envy-freeness for groups: Improved bounds via discrepancy theory
2022, Theoretical Computer ScienceCitation Excerpt :Benabbou et al. [13] examined a group setting where the goods allocated to each group are further divided among the members of the group, so in contrast to our setting, each agent does not derive full utility from the bundle of her group. Several authors studied individual resource allocation using fairness notions relating different groups of agents, for example notions aiming to minimize envy that arises between groups [1,5,14,24,39,62]. We are interested in the following fairness notions:
Almost envy-freeness in group resource allocation
2020, Theoretical Computer ScienceCitation Excerpt :Like us, Ghodsi et al. also considered a model where the groups are not predetermined. Another line of research has also considered group fairness in resource allocation but using a different kind of fairness notions than ours [7,21,37,1,16,3]. In these papers, the resources are allocated to individual agents, and the aim is to minimize the envy that arises between groups of these agents.
Simple fair division of a square
2020, Journal of Mathematical EconomicsDemocratic fair allocation of indivisible goods
2019, Artificial IntelligenceCitation Excerpt :They show that when a rent-division scheme is fixed in advance (e.g., equal or proportional rent division), a unanimously envy-free allocation might not exist, but when the rent can be divided based on the input, such an allocation can always be found. Our group fairness notions differ from those studied, e.g., by Berliant et al. [12], Husseinov [32], Todo et al. [57], Benabbou et al. [10], and Conitzer et al. [23]. In their setting, goods are divided among individuals, each of whom is allocated an individual share.
- ☆
Support provided by National Science Foundation Grants SES-8605629 and SES-8809822 is gratefully acknowledged. The comments of J.H. Boyd III, M. Fleurbaey, Hans Haller, T. ten Raa, S. Tijs, K. Vind, and two anonymous referees have improved the paper. The authors retain full responsibility for any errors. The first draft of this paper was written during the first author's sabbatical at the Department of Economics at the University of California, Berkeley, during 1988–1989. Their kind hospitality and support provided by the University of Rochester are appreciated.