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Fair division among groups[1] (or families[2]) is a class of fair division problems, in which the resources are allocated among groups of agents, rather than among individual agents. After the division, all members in each group consume the same share, but they may have different preferences; therefore, different members in the same group might disagree on whether the allocation is fair or not. Some examples of group fair division settings are:
Several siblings inherited some houses from their parents and have to divide them. Each sibling has a family, whose members may have different opinions regarding which house is better.
A partnership is dissolved, and its assets should be divided among the partners. The partners are firms; each firm has several stockholders, who might disagree regarding which asset is more important.
The university management wants to allocate some meeting-rooms among its departments. In each department there are several faculty members, with differing opinions about which rooms are better.
Two neighboring countries want to divide a disputed region among them. The citizens in each country differ on which parts of the region are more important. This is a common obstacle to resolving international disputes.
The "group of agents" may also represent different conflicting preferences of a single person. As observed in behavioral economics, people often change their preferences according to different frames of mind or different moods.[3] Such people can be represented as a group of agents, each of whom has a different preference.
In all the above examples, the groups are fixed in advance. In some settings, the groups can be determined ad-hoc, that is, people can be grouped based on their preferences. An example of such a setting is:[4]
Some 30 people want to use the local basketball court. Each game involves 10 players with different preferences regarding which time is better. It is required to partition the time of day into 3 parts and partition the players into 3 groups and assign a group to each time-slot.
^Suksompong, Warut (2018). Resource allocation and decision making for groups (Thesis). OCLC 1050345365.
^Segal-Halevi, Erel; Nitzan, Shmuel (December 2019). "Fair cake-cutting among families" (PDF). Social Choice and Welfare. 53 (4): 709–740. doi:10.1007/s00355-019-01210-9. S2CID 1602396.
^Bade, Sophie; Segal-Halevi, Erel (2023-09-01). "Fairness for multi-self agents". Games and Economic Behavior. 141: 321–336. arXiv:1811.06684. doi:10.1016/j.geb.2023.06.004. ISSN 0899-8256.
^Segal-Halevi, Erel; Suksompong, Warut (2 January 2021). "How to Cut a Cake Fairly: A Generalization to Groups". The American Mathematical Monthly. 128 (1): 79–83. arXiv:2001.03327. doi:10.1080/00029890.2021.1835338. S2CID 210157034.
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