# Category: Cake-cutting

Equitable cake-cutting
Equitable (EQ) cake-cutting is a kind of a fair cake-cutting problem, in which the fairness criterion is equitability. It is a cake-allocation in which the subjective value of all partners is the same
Proportional cake-cutting
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, namely, that every partner feels that hi
Efficient cake-cutting
Efficient cake-cutting is a problem in economics and computer science. It involves a heterogeneous resource, such as a cake with different toppings or a land with different coverings, that is assumed
Individual pieces set
In the theory of fair cake-cutting, the individual-pieces set (IPS)is a geometric object that represents all possible utility vectors in cake partitions.
Selfridge–Conway procedure
The Selfridge–Conway procedure is a discrete procedure that produces an envy-free cake-cutting for three partners. It is named after John Selfridge and John Horton Conway. Selfridge discovered it in 1
Even–Paz protocol
The Even–Paz algorithm is an computationally-efficient algorithm for fair cake-cutting. It involves a certain heterogeneous and divisible resource, such as a birthday cake, and n partners with differe
Piecewise-constant valuation
A piecewise-constant valuation is a kind of a function that represents the utility of an agent over a continuous resource, such as land. It occurs when the resource can be partitioned into a finite nu
Egalitarian cake-cutting
Egalitarian cake-cutting is a kind of fair cake-cutting in which the fairness criterion is the egalitarian rule. The cake represents a continuous resource (such as land or time), that has to be alloca
Levmore–Cook moving-knives procedure
The Levmore–Cook moving-knives procedure is a procedure for envy-free cake-cutting among three partners. It is named after Saul X. Levmore and Elizabeth Early Cook who presented it in 1981.It assumes
Barbanel–Brams moving-knives procedure
The Barbanel–Brams rotating-knife procedure is a procedure for envy-free cake-cutting of a cake among three partners. It makes only two cuts, so each partner receives a single connected piece. Its mai
Fair pie-cutting
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 a birthday cake shaped as a disk. The cake should
Utilitarian cake-cutting
Utilitarian cake-cutting (also called maxsum cake-cutting) is a rule for dividing a heterogeneous resource, such as a cake or a land-estate, among several partners with different cardinal utility func
Brams–Taylor–Zwicker procedure
The Brams–Taylor–Zwicker procedure is a protocol for envy-free cake-cutting among 4 partners. The procedure uses a variation of Austin's procedure for two partners and general fractions. That procedur
Strongly-proportional division
A strongly-proportional division (sometimes called super-proportional division) is a kind of a fair division. It is a division of resources among n partners, in which the value received by each partne
Super envy-freeness
A super-envy-free division is a kind of a fair division. It is a division of resources among n partners, in which each partner values his/her share at strictly more than his/her due share of 1/n of th
Truthful cake-cutting
Truthful cake-cutting is the study of algorithms for fair cake-cutting that are also truthful mechanisms, i.e., they incentivize the participants to reveal their true valuations to the various parts o
Simmons–Su protocols
The Simmons–Su protocols are several protocols for envy-free division. They are based on Sperner's lemma. The merits of these protocols is that they put few restrictions on the preferences of the part
Stromquist moving-knives procedure
The Stromquist moving-knives procedure is a procedure for envy-free cake-cutting among three players. It is named after who presented it in 1980. This procedure was the first envy-free moving knife pr
Brams–Taylor procedure
The Brams–Taylor procedure (BTP) is a procedure for envy-free cake-cutting. It explicated the first finite procedure to produce an envy-free division of a cake among any positive integer number of pla
Robertson–Webb query model
In computer science, the Robertson–Webb (RW) query model is a model of computation used by algorithms for the problem of fair cake-cutting. In this problem, there is a resource called a "cake", and se
Cake theory
Cake theory (simplified Chinese: 蛋糕论; traditional Chinese: 蛋糕論; pinyin: Dàngāo lùn) is a metaphor about economic development and the redistribution of wealth in the political discourse of China. It em
Last diminisher
The last diminisher procedure is a procedure for fair cake-cutting. It involves a certain heterogenous and divisible resource, such as a birthday cake, and n partners with different preferences over d
Divide and choose
Divide and choose (also Cut and choose or I cut, you choose) is a procedure for fair division of a continuous resource, such as a cake, between two parties. It involves a heterogeneous good or resourc
Edmonds–Pruhs protocol
Edmonds–Pruhs protocol is a protocol for fair cake-cutting. Its goal is to create a partially proportional division of a heterogeneous resource among n people, such that each person receives a subset
Weller's theorem
Weller's theorem is a theorem in economics. It says that a heterogeneous resource ("cake") can be divided among n partners with different valuations in a way that is both Pareto-efficient (PE) and env
Lone divider
The lone divider procedure is a procedure for proportional cake-cutting. It involves a heterogenous and divisible resource, such as a birthday cake, and n partners with different preferences over diff
Moving-knife procedure
In the mathematics of social science, and especially game theory, a moving-knife procedure is a type of solution to the fair division problem. The canonical example is the division of a cake using a k
Fink protocol
The Fink protocol (also known as Successive Pairs or Lone Chooser) is a protocol for proportional division of a cake. Its main advantage is that it can work in an online fashion, without knowing the n
Proportional cake-cutting with different entitlements
In the fair cake-cutting problem, the partners often have different entitlements. For example, the resource may belong to two shareholders such that Alice holds 8/13 and George holds 5/13. This leads
Robertson–Webb envy-free cake-cutting algorithm
The Robertson–Webb protocol is a protocol for envy-free cake-cutting which is also near-exact. It has the following properties: * It works for any number (n) of partners. * It works for any set of w
Symmetric fair cake-cutting
Symmetric fair cake-cutting is a variant of the fair cake-cutting problem, in which fairness is applied not only to the final outcome, but also to the assignment of roles in the division procedure. As
Stromquist–Woodall theorem
The Stromquist–Woodall theorem is a theorem in fair division and measure theory. Informally, it says that, for any cake, for any n people with different tastes, and for any fraction r, there exists a
Fair cake-cutting
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 to be divisible – it is possible to cut arb
Hill–Beck land division problem
The following variant of the fair cake-cutting problem was introduced by Ted Hill in 1983. There is a territory D adjacent to n countries. Each country values the different subsets of D differently. T
Exact division
Exact division, also called consensus division, is a partition of a continuous resource ("cake") into some k pieces, such that each of n people with different tastes agree on the value of each of the
Chore division
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 is the mirror-image of the fair cake-cutting pro