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Partial Allocation Mechanism
The Partial Allocation Mechanism (PAM) is a mechanism for truthful resource allocation. It is based on the ''max-product allocation'' - the allocation maximizing the product of agents' utilities (also known as the Nash-optimal allocation or the Proportionally-Fair solution; in many cases it is equivalent to the competitive equilibrium from equal incomes). It guarantees to each agent at least 0.368 of his/her utility in the max-product allocation. It was designed by Cole, Gkatzelis and Goel. Setting There are ''m'' resources that are assumed to be ''homogeneous'' and ''divisible''. There are ''n'' agents, each of whom has a personal function that attributes a numeric value to each "bundle" (combination of resources). The valuations are assumed to be homogeneous functions. The goal is to decide what "bundle" to give to each agent, where a bundle may contain a fractional amount of each resource. Crucially, some resources may have to be discarded, i.e., free disposal In various pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truthful Resource Allocation
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. Model There are ''m'' resources that are assumed to be ''homogeneous'' and ''divisible''. Examples are: * Materials, such as wood or metal; * Virtual resources, such as CPU time or computer memory; * Financial resources, such as shares in firms. There are ''n'' agents. Each agent has a function that attributes a numeric value to each "bundle" (combination of resources). It is often assumed that the agents' value functions are ''linear'', so that if the agent receives a fraction ''rj'' of each resource ''j'', then his/her value is the sum of ''rj'' *''vj'' . Design goals The goal is to design a truthful mechanism, that will induce the agents to reveal their true value functions, and then calculate an allocation that satisfies some fairness and efficiency objectives. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Competitive Equilibrium
Competitive equilibrium (also called: Walrasian equilibrium) is a concept of economic equilibrium introduced by Kenneth Arrow and Gérard Debreu in 1951 appropriate for the analysis of commodity markets with flexible prices and many traders, and serving as the benchmark of efficiency in economic analysis. It relies crucially on the assumption of a competitive environment where each trader decides upon a quantity that is so small compared to the total quantity traded in the market that their individual transactions have no influence on the prices. Competitive markets are an ideal standard by which other market structures are evaluated. Definitions A competitive equilibrium (CE) consists of two elements: * A price function P. It takes as argument a vector representing a bundle of commodities, and returns a positive real number that represents its price. Usually the price function is linear - it is represented as a vector of prices, a price for each commodity type. * An allocation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Homogeneous Function
In mathematics, a homogeneous function is a function of several variables such that, if all its arguments are multiplied by a scalar, then its value is multiplied by some power of this scalar, called the degree of homogeneity, or simply the ''degree''; that is, if is an integer, a function of variables is homogeneous of degree if :f(sx_1,\ldots, sx_n)=s^k f(x_1,\ldots, x_n) for every x_1, \ldots, x_n, and s\ne 0. For example, a homogeneous polynomial of degree defines a homogeneous function of degree . The above definition extends to functions whose domain and codomain are vector spaces over a field : a function f : V \to W between two -vector spaces is ''homogeneous'' of degree k if for all nonzero s \in F and v \in V. This definition is often further generalized to functions whose domain is not , but a cone in , that is, a subset of such that \mathbf\in C implies s\mathbf\in C for every nonzero scalar . In the case of functions of several real variables and re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 resources have to be divided fairly, but some of the resources may be left undivided, discarded or donated. Examples of situations with free disposal are allocation of food, clothes jewels etc. Examples of situations ''without'' free disposal are: * Chore division - since all chores must be done. * Allocation of land with an old structure - since the structure may have to be destructed, and destruction is costly. * Allocation of an old car - since the car may have to be carried away to used cars garage, and moving it may be costly. * Allocation of shares in a firm that may have debts - since the firm cannot be disposed of without paying its debts first. The free disposal assumption may be useful for several reasons: * It enables truthful cake-cutting algorithms: The option to discard some o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truthful Mechanism
In game theory, an asymmetric game where players have private information is said to be strategy-proof or strategyproof (SP) if it is a weakly-dominant strategy for every player to reveal his/her private information, i.e. given no information about what the others do, you fare best or at least not worse by being truthful. SP is also called truthful or dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility. An SP game is not always immune to collusion, but its robust variants are; with group strategyproofness no group of people can collude to misreport their preferences in a way that makes every member better off, and with strong group strategyproofness no group of people can collude to misreport their preferences in a way that makes at least one member of the group better off without making any of the remaining members worse off. Examples Typical examples of SP mechanisms are majority voting between two alternatives, secon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Envy-freeness
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 person should receive a share that is, in their eyes, at least as good as the share received by any other agent. In other words, no person should feel envy. General definitions Suppose a certain resource is divided among several agents, such that every agent i receives a share X_i. Every agent i has a personal preference relation \succeq_i over different possible shares. The division is called envy-free (EF) if for all i and j: :::X_i \succeq_i X_j Another term for envy-freeness is no-envy (NE). If the preference of the agents are represented by a value functions V_i, then this definition is equivalent to: :::V_i(X_i) \geq V_i(X_j) Put another way: we say that agent i ''envies'' agent j if i prefers the piece of j over his own piece, i.e.: :::X_i \prec_i X_j :::V_i(X_i) 2 the problem is much harder. See envy-free cake-cutting. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vickrey–Clarke–Groves Mechanism
In mechanism design, a Vickrey–Clarke–Groves (VCG) mechanism is a generic truthful mechanism for achieving a socially-optimal solution. It is a generalization of a Vickrey–Clarke–Groves auction. A VCG auction performs a specific task: dividing items among people. A VCG ''mechanism'' is more general: it can be used to select any outcome out of a set of possible outcomes. Notation There is a set X of possible outcomes. There are n agents which have different valuations for each outcome. The valuation of agent i is represented as a function: : v_i : X \longrightarrow R_+ which expresses the value it has for each alternative, in monetary terms. It is assumed that the agents have Quasilinear utility functions; this means that, if the outcome is x and in addition the agent receives a payment p_i (positive or negative), then the total utility of agent i is: : u_i := v_i(x) + p_i Our goal is to select an outcome that maximizes the sum of values, i.e.: : x^(v) = \arg\max_ \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fair Division Protocols
A fair (archaic: faire or fayre) is a gathering of people for a variety of entertainment or commercial activities. Fairs are typically temporary with scheduled times lasting from an afternoon to several weeks. Types Variations of fairs include: * Art fairs, including art exhibitions and arts festivals * County fair (USA) or county show (UK), a public agricultural show exhibiting the equipment, animals, sports and recreation associated with agriculture and animal husbandry. * Festival, an event ordinarily coordinated with a theme e.g. music, art, season, tradition, history, ethnicity, religion, or a national holiday. * Health fair, an event designed for outreach to provide basic preventive medicine and medical screening * Historical reenactments, including Renaissance fairs and Dickens fairs * Horse fair, an event where people buy and sell horses. * Job fair, event in which employers, recruiters, and schools give information to potential employees. * Regional or state fair, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
