Finding maxmin allocations in cooperative and competitive fair division

Dall’Aglio, Marco; Luca, Camilla Di

doi:10.1007/s10479-014-1611-9

Cited by 8 publications

(5 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They define a group-envy-free division as a division in which no coalition of individuals can take the pieces allocated to another coalition with the same number of individuals and re-divide the pieces among its members such that all members are weakly better-off. Coalitions in cake-cutting are also studied by Dall'Aglio and Di Luca (2014).…”

Section: Dividing Other Kinds Of Resources Among Familiesmentioning

confidence: 99%

Fair cake-cutting among families

Segal-Halevi

Nitzan

2019

Soc Choice Welf

View full text Add to dashboard Cite

We study the fair division of a continuous resource, such as a landestate or a time-interval, among pre-specified groups of agents, such as families. Each family is given a piece of the resource and this piece is used simultaneously by all family members, while different members may have different value functions. Three ways to assess the fairness of such a division are examined. (a) Average Fairness means that each family's share is fair according to the "family value function", defined as the arithmetic mean of the value functions of the family members. (b) Unanimous Fairness means that all members in all families feel that their family's share is fair according to their personal value function. (c) Democratic Fairness means that in each family, at least a fixed fraction (e.g. a half) of the members feel that their family's share is fair. We compare these criteria based on the number of connected components in the resulting division and on their compatibility with Pareto-efficiency.

show abstract

Section: Dividing Other Kinds Of Resources Among Familiesmentioning

confidence: 99%

Fair cake-cutting among families

Segal-Halevi

Nitzan

2019

Soc Choice Welf

View full text Add to dashboard Cite

show abstract

“…Subgradient methods are usually used without any formal stopping criteria since these are problem specific. Dall'Aglio and Di Luca [15] provide two stopping criteria for the subgradient method for fair division: until max…”

Section: B Proposed Methodologymentioning

confidence: 99%

“…Dall'Aglio and Di Luca [15] provided an algorithm that solves the dual problem by using the subgradient method [16] and exploiting the fact that optimal allocations are equitable when the utilities are mutually absolutely continuous. In the next section we will provide a formulation of the task subdivision problem that fits nicely with the fair subdivision background.…”

Section: Introductionmentioning

confidence: 99%

Fair subdivision of multi-robot tasks

Higuera

Dudek

2013

2013 IEEE International Conference on Robotics and Automation

View full text Add to dashboard Cite

We study the problem of distributing a single global task between a group of heterogeneous robots. We view this problem as a fair division game. In this setting, every robot defines a preference function over parts of the task according to its sensing and motion capabilities. These preferences are described by density functions over the task. With such interpretation, we want to find an allocation of the global task that maximizes the probability of task completion. We first formulate the task distribution problem as a fair subdivision problem and provide a centralized algorithm to compute the allocations for each robot. We provide a complexity analysis and computational results of the algorithm.

show abstract

“…(a) One notion of group-fairness involves the standard resource-allocation setting in which each individual receives an individual bundle (Berliant et al, 1992;Hüsseinov, 2011;Dall'Aglio et al, 2009;Dall'Aglio and Di Luca, 2014;Todo et al, 2011;Mouri et al, 2012). A group-envy-free division is defined as a division in which no coalition of individuals can take the pieces allocated to another coalition with the same number of individuals and re-divide the pieces among its members such that all members are weakly better-off.…”

Section: Families and Groupsmentioning

confidence: 99%

Fairness for Multi-Self Agents

Bade¹,

Segal-Halevi²

2018

Preprint

View full text Add to dashboard Cite

Fair division theory mostly involves individual consumption. But resources are often allocated to groups, such as families or countries, whose members consume the same bundle but have different preferences. Do fair and efficient allocations exist in such an "economy of families"?We adapt three common notions of fairness: fair-share, no-envy and egalitarian-equivalence, to an economy of families. The stronger adaptation -individual fairness -requires that each individual in each family perceives the division as fair; the weaker one -family fairness -requires that the family as a whole, treated as a single agent with (typically) incomplete preferences, perceives the division as fair. Individual-fair-share, family-no-envy and family-egalitarianequivalence are compatible with efficiency under broad conditions. The same holds for individual-no-envy when there are only two families. In contrast, individual-no-envy with three or more families and individual-egalitarian-equivalence with two or more families are typically incompatible with efficiency, unlike the situation in an economy of individuals. The common market equilibrium approach to fairness is of limited use in economies with families. In contrast, the leximin approach is broadly applicable: it yields an efficient, individual-fairshare, and family-egalitarian-equivalent allocation.

show abstract

Finding maxmin allocations in cooperative and competitive fair division

Cited by 8 publications

References 18 publications

Fair cake-cutting among families

Fair cake-cutting among families

Fair subdivision of multi-robot tasks

Fairness for Multi-Self Agents

Contact Info

Product

Resources

About