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Problem of sharing resources
Fair division is an optimisation problem in game theory of dividing a set of resources among several parties who have an entitlement to them so that each
Fair_division
This page lists notable open problems related to fair division - a field in the intersection of mathematics, computer science, political science and economics
List of unsolved problems in fair division
List_of_unsolved_problems_in_fair_division
Game theory problem
Strategic fair division studies problems of fair division, in which participants cooperate to subdivide goods or resources fairly, from a point of view
Strategic_fair_division
Value that a party would ideally get
In fair division, a person's entitlement is the value of the goods they are owed or deserve, i.e. the total value of the goods or resources that a player
Entitlement_(fair_division)
Probabilistic model of fair resource allocation
Boltzmann Fair Division is a probabilistic model of resource allocation inspired by the Boltzmann distribution in statistical mechanics. The model introduces
Boltzmann_Fair_Division
Fair division problem
Fair cake-cutting is a kind of fair division problem. The problem involves a heterogeneous resource, such as a cake with different toppings, that is assumed
Fair_cake-cutting
Scientific tests related to game theory
Various experiments have been made to evaluate various procedures for fair division, the problem of dividing resources among several people. These include
Fair_division_experiments
Weakly optimal allocation of resources
Computation. Sandomirskiy, Fedor; Segal-Halevi, Erel (2022). "Efficient Fair Division with Minimal Sharing". Operations Research. 70 (3): 1762–1782. arXiv:1908
Pareto_efficiency
Temporal fair division is a sequence of fair division instances among the same set of agents. Some examples are: A group of housemates that have to divide
Temporal_fair_division
Fair division among groups (or families) is a class of fair division problems, in which the resources are allocated among groups of agents, rather than
Fair_division_among_groups
Data network scheduling algorithm
Proportional-fair scheduling is a compromise-based scheduling algorithm. It is based upon maintaining a balance between two competing interests: Trying
Proportional-fair_scheduling
Topics referred to by the same term
algorithms Fairness (machine learning), a desirable property of machine learning algorithms Fair division in game theory Fair value in economics Fairness of human
Fairness
Network scheduling algorithm
first appears in. Deficit round robin Fairness measure Max-min fairness Scheduling algorithm Statistical time division multiplexing Weighted round robin Parekh
Weighted_fair_queueing
Probability distribution of energy states of a system
emissions trading. A new allocation method, known as the Boltzmann Fair Division, uses the Boltzmann distribution to describe the most probable, natural
Boltzmann_distribution
Fair division class using unique allocation methods
Online fair division is a class of fair division problems in which the resources, or the people to whom they should be allocated, or both, are not all
Online_fair_division
Solution to the fair division problem
a moving-knife procedure is a type of solution to the fair division problem. "Fair division" is the problem in game theory of dividing a set of resources
Moving-knife_procedure
List of unsolved problems in economics List of unsolved problems in fair division List of unsolved problems in statistics List of unsolved problems in
Lists_of_problems
Problem in game theory
Fair river sharing is a kind of a fair division problem in which the waters of a river has to be divided among countries located along the river. It differs
Fair_river_sharing
Fair division protocol in computing
Dominant resource fairness (DRF) is a rule for fair division. It is particularly useful for dividing computing resources in among users in cloud computing
Dominant_resource_fairness
A proportional division is a kind of fair division in which a resource is divided among n partners with subjective valuations, giving each partner at
Proportional_division
Fair division problem for discrete items
Fair item allocation is a kind of the fair division problem in which the items to divide are discrete rather than continuous. The items have to be divided
Fair_item_allocation
In the theory of fair division, the price of fairness (POF) is the ratio of the largest economic welfare attainable by a division to the economic welfare
Price_of_fairness
One over a whole number
the tangencies of Ford circles. Unit fractions are commonly used in fair division, and this familiar application is used in mathematics education as an
Unit_fraction
Mathematical problem
mathematician Gábor Simonyi shows that the two thieves can achieve an almost fair division in the following sense. If the necklace is arranged so that no t-split
Necklace_splitting_problem
Concept in game theory
doi:10.1016/S0165-0114(97)00168-1. ISSN 0165-0114. Hervé Moulin (2004). Fair Division and Collective Welfare. Cambridge, Massachusetts: MIT Press. ISBN 9780262134231
Shapley_value
Fair division of a single homogeneous resource is one of the simplest settings in fair division problems. There is a single resource that should be divided
Fair division of a single homogeneous resource
Fair_division_of_a_single_homogeneous_resource
Type of fair division
Efficiency and fairness are two major goals of welfare economics. Given a set of resources and a set of agents, the goal is to divide the resources among
Efficient_envy-free_division
Infinite binary sequence generated by repeated complementation and concatenation
obtained thus far. It is sometimes called the fair share sequence because of its applications to fair division or parity sequence. The first few steps of
Thue–Morse_sequence
Economic concept of fairness
Economic equity is the construct, concept or idea of fairness in economics and justice in the distribution of wealth, resources, and taxation within a
Equity_(economics)
Criterion for evaluating rules for fair division
criterion for evaluating rules for fair division. Coherence requires that the outcome of a fairness rule is fair not only for the overall problem, but
Coherence_(fairness)
Necklace splitting problem
such that all partners agree that the parts have the same value. This fair-division challenge is sometimes referred to as the consensus-halving problem
Hobby–Rice_theorem
Measure theory theorems
of fair cake-cutting. They were published by Lester Dubins and Edwin Spanier in 1961. Although the original motivation for these theorems is fair division
Dubins–Spanier_theorems
Rule for balancing a game with an advantage when going first
that or switch colors with the other player. This leads players to choose fair komi amounts because if they choose a komi that is too advantageous, the
Pie_rule
Problem in probability theory
is not merely one of calculation; it also involves deciding what a "fair" division actually is. Luca Pacioli considered such a problem in his 1494 textbook
Problem_of_points
Computer scientist
aspects of game theory, social choice, and fair division. He is the founder of Spliddit, a fair division website. Procaccia received his Ph.D., summa
Ariel_D._Procaccia
Type of optimization problem
Chore division is a fair division problem in which the divided resource is undesirable, so that each participant wants to get as little as possible. It
Chore_division
Problem of fair division
Rental harmony is a kind of a fair division problem in which indivisible items and a fixed monetary cost have to be divided simultaneously. The housemates
Rental_harmony
Concept relating to distribution of rewards to group members
need. The Boltzmann fair division framework has been shown to bridge classical theories and practical policy applications, enabling fair and efficient distributions
Distributive_justice
Topics referred to by the same term
Proportional division, a kind of fair division Percentage, a number or ratio expressed as a fraction of 100 Proportional fonts Proportionally fair, a scheduling
Proportionality
(1996). Fair Division: From cake-cutting to dispute resolution. pp. 116–120. ISBN 0521556449. Brams, Steven J.; Taylor, Alan D. (1996). Fair Division [From
Selfridge–Conway_procedure
Fair division in law
a method of allocating profit earned or loss incurred Fair division Entitlement (fair division) Proportional cake-cutting with different entitlements
Apportionment
Theorem on triangulation graph colorings
of fixed points and in root-finding algorithms, and are applied in fair division (cake cutting) algorithms. According to the Soviet Mathematical Encyclopaedia
Sperner's_lemma
Polish mathematician (1887–1972)
distributed". While in hiding during World War II, Steinhaus worked on the fair cake-cutting problem: how to divide a heterogeneous resource among several
Hugo_Steinhaus
In the fair cake-cutting problem, the partners often have different entitlements. For example, the resource may belong to two shareholders such that Alice
Proportional cake-cutting with different entitlements
Proportional_cake-cutting_with_different_entitlements
In fair division problems, spite is a phenomenon that occurs when a player's value of an allocation decreases when one or more other players' valuation
Spite_(game_theory)
Topics referred to by the same term
nothing can be improved without something else being hurt Efficiency (fair division), any changes made to assist one person would harm another Efficiency
Efficiency_(disambiguation)
Two-person envy-free cake-cutting method
choose (also cut and choose or I cut, you choose) is a procedure for fair division of a continuous resource between two parties. It involves a heterogeneous
Divide_and_choose
Axiom of decision theory and social sciences
variety of fields, including economics, cognitive science, social choice, fair division, rational choice, artificial intelligence, probability, and game theory
Independence of irrelevant alternatives
Independence_of_irrelevant_alternatives
Fair division problem
Fair random assignment (also called probabilistic one-sided matching) is a kind of a fair division problem. In an assignment problem (also called house-allocation
Fair_random_assignment
Division problem
The fair pie-cutting problem is a variation of the fair cake-cutting problem, in which the resource to be divided is circular. As an example, consider
Fair_pie-cutting
cake-cutting with connected pieces. Simmons' algorithm is one of the few fair division algorithms which have been implemented and put online. One nice thing
Simmons–Su_protocols
Algorithm for allocating divisible objects
was developed by Hervé Moulin and Anna Bogomolnaia as a solution for the fair random assignment problem, where the fraction that each agent receives of
Simultaneous_eating_algorithm
Pathological behavior by an apportionment rule
to discrete values. Several paradoxes related to apportionment and fair division have been identified. In some cases, simple adjustments to an apportionment
Apportionment_paradox
English association football league
Beginning with the 2012–13 season, a Financial Fair Play arrangement has been in place in all three divisions of the Football League, the intention being
EFL_League_One
Topics referred to by the same term
or upset without self-benefit Spite (game theory), a phenomenon in fair division economics problems Spite (punk band), a hardcore punk band from Michigan
Spite
Principle in Bayesian statistics
applied in economics and resource allocation. For example, the Boltzmann fair division model uses the maximum entropy (Boltzmann) distribution to allocate
Principle_of_maximum_entropy
and envy free cake division". Ars Combinatoria. 45: 97–108. Robertson, Jack; Webb, William (1998). Cake-Cutting Algorithms: Be Fair If You Can. Natick
Robertson–Webb envy-free cake-cutting algorithm
Robertson–Webb_envy-free_cake-cutting_algorithm
Fair item allocation procedure
Round robin is a procedure for fair item allocation. It can be used to allocate several indivisible items among several people, such that the allocation
Round-robin_item_allocation
Topics referred to by the same term
free dictionary. Entitled or Entitlement may refer to: Entitlement (fair division) Entitlement (psychology) Entitlement commodities Entitlement program
Entitlement
American mathematician
area is combinatorics, and he is particularly known for his work on fair division. Su and Michael Starbird are co-authors of the book Topology Through
Francis_Su
Criterion for fair division
envy-freeness (also called: coalition fairness) is a criterion for fair division. A group-envy-free division is a division of a resource among several partners
Group_envy-freeness
Fair cake-cutting procedure
symmetric fair cake-cutting procedure. Fair Division: Method of Lone Divider at Cut-the-Knot. Steinhaus, Hugo (1948). "The problem of fair division". Econometrica
Lone_divider
Type of fair division
receive more than their fair share of 1 / n {\displaystyle 1/n} . An exact division with different weights is not necessarily fair. Going back to the opening
Consensus_splitting
Interdisciplinary research discipline
the theory of linear programming, algorithmic mechanism design, and fair division algorithms. Computational economics developed concurrently with the
Computational_economics
World's fair held in New York City
The 1964 New York World's Fair (also known as the 1964–1965 New York World's Fair) was an international exposition at Flushing Meadows–Corona Park in
1964_New_York_World's_Fair
Procedure for fair item allocation
envy-graph procedure (also called the envy-cycles procedure) is a procedure for fair item allocation. It can be used by several people who want to divide among
Envy-graph_procedure
Retrieved 27 August 2016. Brams, Steven J.; Taylor, Alan D. (1996). Fair division: from cake-cutting to dispute resolution. Cambridge University Press
Levmore–Cook moving-knives procedure
Levmore–Cook_moving-knives_procedure
Criterion of fair item allocation
Maximin share (MMS) is a criterion of fair item allocation. Given a set of items with different values, the 1-out-of-n maximin-share is the maximum value
Maximin_share
Problem in game theory
mathematics and especially game theory, the airport problem is a type of fair division problem in which it is decided how to distribute the cost of an airport
Airport_problem
Distribution procedure
priority (RP), also called random serial dictatorship (RSD), is a procedure for fair random assignment - dividing indivisible items fairly among people. Suppose
Random priority item allocation
Random_priority_item_allocation
American economist (born 1942)
business cycle theory and the theory of distribution). In the field of fair division, he is considered the first to introduce the concept of envy-free resource
Duncan_K._Foley
Mathematical principles
In mathematics and fair division, apportionment problems involve dividing (apportioning) a whole number of identical goods fairly across several parties
Mathematics_of_apportionment
American basketball player (born 2001)
Dyaisha Cheryce Fair (born August 7, 2001) is an American professional basketball player who is a free agent. Fair was the 16th overall pick in the 2024
Dyaisha_Fair
Game Theory variant
countries would like to divide D fairly among them, where "fair" means a proportional division. Additionally, the share allocated to each country must be
Hill–Beck land division problem
Hill–Beck_land_division_problem
resource, as in fair cake-cutting. Determining the optimal locations of supply depots; Maximizing the surveillance coverage. Fair division of land has been
Map_segmentation
French mathematician (born 1950)
particular in the fields of mechanism design, social choice, game theory and fair division. He has written five books and over 100 peer-reviewed articles. Moulin
Hervé_Moulin
Rule for fair division of invisible items
Rank-maximal (RM) allocation is a rule for fair division of indivisible items. Suppose we have to allocate some items among people. Each person can rank
Rank-maximal_allocation
Problem in mathematical sociology
by an allocation rule that takes history into account. Entitlement (fair division) Proportional cake-cutting with different entitlements Strategic bankruptcy
Bankruptcy_problem
Model of computation used by algorithms
general - be given as inputs to a fair division algorithm. The RW model specifies two kinds of queries that a fair division algorithm may ask the agents: Eval
Robertson–Webb_query_model
Problems with resource sharing in a group
resources are limited, groups need to decide on fair ways of apportioning them out to their members. These fairness judgments are determined by procedural and
Fairness_dilemmas
Annual event
Organizationally, the fair is one of the divisions of the Colorado Department of Agriculture. When Colorado became a state in 1876, its state fair was already earning
Colorado_State_Fair
Fair allocation of items and money is a class of fair item allocation problems in which, during the allocation process, it is possible to give or take
Fair allocation of items and money
Fair_allocation_of_items_and_money
Criterion for fair division
Envy-freeness, also known as no-envy, is a criterion for fair division. It says that, when resources are allocated among people with equal rights, each
Envy-freeness
Study of fair cake-cutting with true valuations
mechanisms that are fair ex-post and not just ex-ante. Several such mechanisms have been developed. An exact division (aka consensus division) is a partition
Truthful_cake-cutting
Envy-free solution to the cake-cutting problem
necessarily efficient. In a simpler version of the problem, a division is regarded as "fair" if all people ("players") are satisfied that each has received
Stromquist moving-knives procedure
Stromquist_moving-knives_procedure
Procedure of fair division
theorem Robertson, Jack; Webb, William (1998). Cake-Cutting Algorithms: Be Fair If You Can. Natick, Massachusetts: A. K. Peters. ISBN 978-1-56881-076-8.
Robertson–Webb rotating-knife procedure
Robertson–Webb_rotating-knife_procedure
Annual event in Oregon, United States
running the fair was delegated to the Oregon State Parks and Recreation Department, and the division is now known as the Oregon State Fair & Exposition
Oregon_State_Fair
Pierre de Fermat and Blaise Pascal (1654) on such questions as the fair division of the stake in an interrupted game of chance. Christiaan Huygens (1657)
History_of_probability
Comparison between vectors
leximin order is particularly important in social choice theory and fair division. A vector x = (x1, ..., xn) is leximin-larger than a vector y = (y1
Leximin_order
Procedures for equitable division of a cake
JSTOR 3616548. S2CID 158398839. Brams, Steven J.; Taylor, Alan D. (1996). Fair Division [From cake-cutting to dispute resolution]. pp. 22–27. ISBN 978-0-521-55644-6
Austin moving-knife procedures
Austin_moving-knife_procedures
Topics referred to by the same term
Antártica Chilena, Chile Weighted proportionality (WPR), in fair cake-cutting, a kind of fair-division problem WPR Records, a music label founded in 2004 by
WPR
Mathematical subject
many equivalent versions and analogs and has been used in the study of fair division problems. In another application of homological methods to graph theory
Topological_combinatorics
American mathematician (born 1943)
secretary problem and prophet inequality) and of fair division, in particular the Hill–Beck land division problem. Hill has attracted widespread attention
Ted_Hill_(mathematician)
Fair division problem
the entire Vanilla to George. The maxsum is 13. The utilitarian division is not fair: it is not proportional since George receives less than half the
Utilitarian_cake-cutting
State government agency in the United States
California Civil Rights Department (CRD), formerly known as the Department of Fair Employment and Housing (DFEH), is an agency of California state government
California Civil Rights Department
California_Civil_Rights_Department
(also called weights) in rules of apportionment, or in algorithms of fair division with different entitlements. Fractional approval voting is a special
Fractional_approval_voting
Method of resource allocation
Brams, Steven J.; Edelman, Paul H.; Fishburn, Peter C. (2003-09-01). "Fair Division of Indivisible Items". Theory and Decision. 55 (2): 147–180. doi:10
Ordinal_Pareto_efficiency
Annual state fair
March. The fair has been held at the Ohio Expo Center and State Fairgrounds since 1886. Patrollers include security guards, the Columbus Division of Police
Ohio_State_Fair
Type of fair division
A proportional cake-cutting is a kind of fair cake-cutting. It is a division of a heterogeneous resource ("cake") that satisfies the proportionality criterion
Proportional_cake-cutting
Russian economist
Bogomolnaia, Anna; Moulin, Hervé; Sandomirskiy, Fedor (2022). "On the fair division of a random object". Management Science. 68 (2): 809–1589. arXiv:1903
Anna_Bogomolnaia
FAIR DIVISION
FAIR DIVISION
Boy/Male
Indian
Excellent, Outstanding
Female
Welsh
Welsh form of Greek Maria, MAIR means "obstinacy, rebelliousness" or "their rebellion."
Male
English
Variant spelling of English Gare, GAIR means "spear."
Boy/Male
Indian
Surpassing, Excellent, Leader
Surname or Lastname
English
English : unexplained.
Boy/Male
Muslim
Excellent, Outstanding
Boy/Male
British, English, French, German, Greek, Latin, Swiss
Yellow; Blond; Yellow Hair; Fair Haired
Surname or Lastname
English
English : from Middle English farre ‘bull’, applied as a nickname for a fierce or lusty man or a metonymic occupational name for someone who kept a bull.German : nickname from Middle High German varne, var, with the same meaning as 1.
Boy/Male
Indian
Poor, Needy
Surname or Lastname
Scottish spelling of Irish Hare.English
Scottish spelling of Irish Hare.English : nickname for someone with some peculiarity of the hair, from Middle English here ‘hair’.
Boy/Male
Muslim
Poor, Needy
Male
Hebrew
(×™Ö¸×ִיר) Variant spelling of Hebrew Yaiyr, YAIR means "whom God enlightens."Â
Boy/Male
Hindu
Brave
Boy/Male
Muslim
Walking, Going on foot
Boy/Male
Muslim
Tall, Towering, Lofty
Boy/Male
Indian
Victorious, Triumphant, Gain
Male
English
 Anglicized form of Hebrew Yaiyr, JAIR means "whom God enlightens." In the bible, this is the name of several characters, including a descendant of Manasseh. Anglicized form of Hebrew Yauwr, meaning "forested." In the bible, this is the name of the father of Elhanan.
Surname or Lastname
French
French : habitational name from any of various places in France, deriving their names mostly from Old French fain ‘swamp’, but Latin fanum ‘temple’ is also a source in some cases.English : variant spelling of Fayne.
Surname or Lastname
English
English : nickname meaning ‘handsome’, ‘beautiful’, ‘fair’, Middle English fair, fayr, Old English fæger. The word was also occasionally used as a personal name in Middle English, applied to both men and women.Irish : translation of Gaelic fionn ‘fair’, which Woulfe describes as ‘a descriptive epithet that supplanted the real surname’, or a reduced Anglicized form of Gaelic Mac F(h)inn, a variant of Mag Fhinn (see McGinn).
Boy/Male
Muslim
Surpassing, Excellent, Leader
FAIR DIVISION
FAIR DIVISION
Girl/Female
Arabic, Muslim
Silver
Boy/Male
Hindu
Girl/Female
Muslim
Producing delight
Girl/Female
Tamil
Beloved
Boy/Male
German
Mighty as a Bear
Girl/Female
American, Australian
Combination of Jasmine and Lene
Boy/Male
Hindu, Indian
Show Man
Girl/Female
German English Anglo Saxon Norse Teutonic
noble.
Boy/Male
Indian
Homeland
Girl/Female
British, Christian, Danish, English, French, German, Greek, Latin
A Compound of Lee; Wood; To Twine Around
FAIR DIVISION
FAIR DIVISION
FAIR DIVISION
FAIR DIVISION
FAIR DIVISION
n.
A fair woman; a sweetheart.
superl.
Distinct; legible; as, fair handwriting.
n.
Odoriferous or contaminated air.
n.
A competitive exhibition of wares, farm products, etc., not primarily for purposes of sale; as, the Mechanics' fair; an agricultural fair.
n.
A spring device used in a hair-trigger firearm.
n.
A single thing, composed of two pieces fitted to each other and used together; as, a pair of scissors; a pair of tongs; a pair of bellows.
n.
Hair (human or animal) used for various purposes; as, hair for stuffing cushions.
a.
Given by fairies; as, fairy money.
superl.
Without a dark hue; light; clear; as, a fair skin.
superl.
Free from any marked characteristic; average; middling; as, a fair specimen.
superl.
Free from obstacles or hindrances; unobstructed; unincumbered; open; direct; -- said of a road, passage, etc.; as, a fair mark; in fair sight; a fair view.
a.
Appearing only when times or circumstances are prosperous; as, a fair-weather friend.
n.
A festival, and sale of fancy articles. erc., usually for some charitable object; as, a Grand Army fair.
n.
A number of things resembling one another, or belonging together; a set; as, a pair or flight of stairs. "A pair of beads." Chaucer. Beau. & Fl. "Four pair of stairs." Macaulay. [Now mostly or quite disused, except as to stairs.]
superl.
Not overcast; cloudless; clear; pleasant; propitious; favorable; -- said of the sky, weather, or wind, etc.; as, a fair sky; a fair day.
v. t.
To make fair or beautiful.
a.
Having fair or light-colored hair.
v. i.
Same as To pair off. See phrase below.
superl.
Characterized by frankness, honesty, impartiality, or candor; open; upright; free from suspicion or bias; equitable; just; -- said of persons, character, or conduct; as, a fair man; fair dealing; a fair statement.
n.
Two of a sort; a span; a yoke; a couple; a brace; as, a pair of horses; a pair of oxen.