No-justified-envy matching
In economics and social choice theory, a no-justified-envy matching is a matching in a two-sided market, in which no agent prefers the assignment of another agent and is simultaneously preferred by th
Fair river sharing
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 from other fair division problems in that t
Map segmentation
In mathematics, the map segmentation problem is a kind of optimization problem. It involves a certain geographic region that has to be partitioned into smaller sub-regions in order to achieve a certai
Shapley value
The Shapley value is a solution concept in cooperative game theory. It was named in honor of Lloyd Shapley, who introduced it in 1951 and won the Nobel Memorial Prize in Economic Sciences for it in 20
Kalai–Smorodinsky bargaining solution
The Kalai–Smorodinsky (KS) bargaining solution is a solution to the Bargaining problem. It was suggested by Ehud Kalai and Meir Smorodinsky, as an alternative to Nash's bargaining solution suggested 2
Envy-free pricing
Envy-free pricing is a kind of fair item allocation. There is a single seller that owns some items, and a set of buyers who are interested in these items. The buyers have different valuations to the i
Price of fairness
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 attained by a fair division. The POF is a quan
Efficient envy-free 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 the agents in a way that is both Pareto effici
Fair division
Fair division is the problem in game theory of dividing a set of resources among several people who have an entitlement to them so that each person receives their due share. That problem arises in var
Surplus sharing
Surplus sharing is a kind of a fair division problem where the goal is to share the financial benefits of cooperation (the "economic surplus") among the cooperating agents. As an example, suppose ther
Sperner's lemma
In mathematics, Sperner's lemma is a combinatorial result on colorings of triangulations, analogous to the Brouwer fixed point theorem, which is equivalent to it. It states that every Sperner coloring
Airport problem
In 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 runway among different players who nee
Entitlement (fair division)
Entitlement in fair division describes that proportion of the resources or goods to be divided that a player can expect to receive. In many fair division settings, all agents have equal entitlements,
Problem of the Nile
The problem of the Nile is a mathematical problem related to equal partitions of measures. The problem was first presented by Ronald Fisher in 1936–1938. It is presented by Dubins and Spanier in the f
Rank-maximal allocation
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 the items from best to worst. The RM rule says
Fair division experiments
Various experiments have been made to evaluate various procedures for fair division, the problem of dividing resources among several people. These include case studies, computerized simulations, and l
Bankruptcy problem
A bankruptcy problem, also called a claims problem, is a problem of distributing a homogeneous divisible good (such as money) among people with different claims. The focus is on the case where the amo
Hobby–Rice theorem
In mathematics, and in particular the necklace splitting problem, the Hobby–Rice theorem is a result that is useful in establishing the existence of certain solutions. It was proved in 1965 by Charles
Fair division among groups
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 among individual agents. After the division, all
Online fair division
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 available when the allocation decision is made. S
Fair division of a single homogeneous resource
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 between several people. The challenge is tha
Necklace splitting problem
Necklace splitting is a picturesque name given to several related problems in combinatorics and measure theory. Its name and solutions are due to mathematicians Noga Alon and Douglas B. West. The basi
Spite (game theory)
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 increases. Thus, other things being equal, a pla
Dubins–Spanier theorems
The Dubins–Spanier theorems are several theorems in the theory of fair cake-cutting. They were published by Lester Dubins and Edwin Spanier in 1961. Although the original motivation for these theorems
Pie rule
The pie rule, sometimes referred to as the swap rule, is a rule used to balance abstract strategy games where a first-move advantage has been demonstrated. After the first move is made in a game that
Free disposal
In various parts of economics, the term free disposal implies that resources can be discarded without any cost. For example, a fair division setting with free disposal is a setting where some resource