An envy-free cake-cutting is a kind of fair cake-cutting. It is a division of a heterogeneous resource ("cake") that satisfies the envy-free criterion, namely, that every partner feels that their allocated share is at least as good as any other share, according to their own subjective valuation.
Divide and choose is a procedure for fair division of a continuous resource, such as a cake, between two parties. It involves a heterogeneous good or resource and two partners who have different preferences over parts of the cake. The protocol proceeds as follows: one person cuts the cake into two pieces; the other person selects one of the pieces; the cutter receives the remaining piece.
Adjusted Winner (AW) is a procedure for envy-free item allocation. Given two agents and some goods, it returns a partition of the goods between the two agents with the following properties:
- Envy-freeness: Each agent believes that his share of the goods is at least as good as the other share;
- Equitability: The "relative happiness levels" of both agents from their shares are equal;
- Pareto-optimality: no other allocation is better for one agent and at least as good for the other agent;
- At most one good has to be shared between the agents.
Algorithmic game theory (AGT) is an area in the intersection of game theory and computer science, with the objective of understanding and design of algorithms in strategic environments.
Distributed algorithmic mechanism design (DAMD) is an extension of algorithmic mechanism design.
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 arbitrarily small pieces of it without destroying their value. The resource has to be divided among several partners who have different preferences over different parts of the cake, i.e., some people prefer the chocolate toppings, some prefer the cherries, some just want as large a piece as possible. The division should be unanimously fair - each person should receive a piece that he or she believes to be a fair share.
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 to be divisible - it is possible to cut arbitrarily small pieces of it without destroying their value. The resource has to be divided among several partners who have different preferences over different parts of the cake, i.e., some people prefer the chocolate toppings, some prefer the cherries, some just want as large a piece as possible, etc. The allocation should be economically efficient. Several notions of efficiency have been studied:
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, i.e., each partner is equally happy with his/her share. Mathematically, that means that for all partners i and j:
Fair item allocation is a kind of a fair division problem in which the items to divide are discrete rather than continuous. The items have to be divided among several partners who value them differently, and each item has to be given as a whole to a single person. This situation arises in various real-life scenarios:
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 his allocated share is worth at least 1/n of the total.
A picking sequence is a protocol for fair item assignment. Suppose m items have to be divided among n agents. One way to allocate the items is to let one agent select a single item, then let another agent select a single item, and so on. A picking-sequence is a sequence of m agent-names, where each name determines what agent is the next to pick an item.
The Price of Anarchy (PoA) is a concept in game theory and mechanism design that measures how the social welfare of a system degrades due to selfish behavior of its agents. It has been studied extensively in various contexts, particularly in auctions.
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 lab experiments.
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 of the cake.
Truthful resource allocation is the problem of allocating resources among agents with different valuations over the resources, such that agents are incentivized to reveal their true valuations over the resources.
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 several agents with different value measures on the cake. The goal is to divide the cake among the agents such that each agent will consider his/her piece as "fair" by his/her personal value measure. Since the agents' valuations can be very complex, they cannot - in 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 and Cut. Informally, an Eval query asks an agent to specify his/her value to a given piece of the cake, and a Cut query asks an agent to specify a piece of cake with a given value.
In economics and computer science, Fractional Pareto efficiency or Fractional Pareto optimality (fPO) is a variant of Pareto efficiency used in the setting of fair allocation of discrete objects. An allocation of objects is called discrete if each item is wholly allocated to a single agent; it is called fractional if some objects are split among two or more agents. A discrete allocation is called Pareto-efficient (PO) if it is not Pareto-dominated by any discrete allocation; it is called fractionally Pareto-efficient (fPO) if it is not Pareto-dominated by any discrete or fractional allocation. So fPO is a stronger requirement than PO: every fPO allocation is PO, but not every PO allocation is fPO.
In computational economics, a single-minded agent is an agent who wants only a very specific combination of items. The valuation function of such an agent assigns a positive value only to a specific set of items, and to all sets that contain it. It assigns a zero value to all other sets. A single-minded agent regards the set of items he wants as purely complementary goods.
Fair division among groups 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:
