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Fisher Market
Fisher market is an economic model attributed to Irving Fisher. It has the following ingredients: * A set of m divisible products with pre-specified supplies (usually normalized such that the supply of each good is 1). * A set of n buyers. * For each buyer i=1,\dots,n, there is a pre-specified monetary budget B_i. Each product j has a price p_j; the prices are determined by methods described below. The price of a ''bundle'' of products is the sum of the prices of the products in the bundle. A bundle is represented by a vector x = x_1,\dots,x_m, where x_j is the quantity of product j. So the price of a bundle x is p(x)=\sum_^m p_j\cdot x_j. A bundle is ''affordable'' for a buyer if the price of that bundle is at most the buyer's budget. I.e, a bundle x is affordable for buyer i if p(x)\leq B_i. Each buyer has a preference relation over bundles, which can be represented by a utility function. The utility function of buyer i is denoted by u_i. The ''demand set'' of a buyer is the se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economic Model
An economic model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed to illustrate complex processes. Frequently, economic models posit structural parameters. A model may have various exogenous variables, and those variables may change to create various responses by economic variables. Methodological uses of models include investigation, theorizing, and fitting theories to the world. Overview In general terms, economic models have two functions: first as a simplification of and abstraction from observed data, and second as a means of selection of data based on a paradigm of econometric study. ''Simplification'' is particularly important for economics given the enormous complexity of economic processes. This complexity can be attributed to the diversity of factors that determine economic activity; t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Flow Problem
In Optimization (mathematics), optimization theory, maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow (i.e., flow from Glossary of graph theory#Direction, source s to Glossary of graph theory#Direction, sink t) is equal to the minimum capacity of an Cut (graph theory), s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem. History The maximum flow problem was first formulated in 1954 by Ted Harris (mathematician), T. E. Harris and F. S. Ross as a simplified model of Soviet railway traffic flow. In 1955, Lester R. Ford, Jr. and D. R. Fulkerson, Delbert R. Fulkerson created the first known algorithm, the Ford–Fulkerson algorithm.Ford, L.R., Jr.; Fulkerson, D.R., ''Flows in Networks'', Princeton University Press ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Equilibrium
In economics, general equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that the interaction of demand and supply will result in an overall general equilibrium. General equilibrium theory contrasts with the theory of ''partial'' equilibrium, which analyzes a specific part of an economy while its other factors are held constant. General equilibrium theory both studies economies using the model of equilibrium pricing and seeks to determine in which circumstances the assumptions of general equilibrium will hold. The theory dates to the 1870s, particularly the work of French economist Léon Walras in his pioneering 1874 work ''Elements of Pure Economics''. The theory reached its modern form with the work of Lionel W. McKenzie (Walrasian theory), Kenneth Arrow and Gérard Debreu (Hicksian theory) in the 1950s. Overview Broadly speaking, general equilibrium tries to give a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Almost All
In mathematics, the term "almost all" means "all but a negligible quantity". More precisely, if X is a set (mathematics), set, "almost all elements of X" means "all elements of X but those in a negligible set, negligible subset of X". The meaning of "negligible" depends on the mathematical context; for instance, it can mean finite set, finite, countable set, countable, or null set, null. In contrast, "almost no" means "a negligible quantity"; that is, "almost no elements of X" means "a negligible quantity of elements of X". Meanings in different areas of mathematics Prevalent meaning Throughout mathematics, "almost all" is sometimes used to mean "all (elements of an infinite set) except for finite set, finitely many". This use occurs in philosophy as well. Similarly, "almost all" can mean "all (elements of an uncountable set) except for countable set, countably many". Examples: * Almost all positive integers are greater than 1012. * Almost all prime numbers are odd (2 is the only ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PPAD (complexity)
In computer science, PPAD ("Polynomial Parity Arguments on Directed graphs") is a complexity class introduced by Christos Papadimitriou in 1994. PPAD is a subclass of TFNP based on functions that can be shown to be total by a parity argument. The class attracted significant attention in the field of algorithmic game theory because it contains the problem of computing a Nash equilibrium: this problem was shown to be complete for PPAD by Daskalakis, Goldberg and Papadimitriou with at least 3 players and later extended by Chen and Deng to 2 players.*. Definition PPAD is a subset of the class TFNP, the class of function problems in FNP that are guaranteed to be total. The TFNP formal definition is given as follows: :A binary relation P(''x'',''y'') is in TFNP if and only if there is a deterministic polynomial time algorithm that can determine whether P(''x'',''y'') holds given both ''x'' and ''y'', and for every ''x'', there exists a ''y'' such that P(''x'',''y'') holds. Subclasses ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Approximate Competitive Equilibrium From Equal Incomes
Approximate Competitive Equilibrium from Equal Incomes (A-CEEI) is a procedure for fair item assignment. It was developed by Eric Budish. Background CEEI (Competitive Equilibrium from Equal Incomes) is a fundamental rule for fair division of divisible resources. It divides the resources according to the outcome of the following hypothetical process: * Each agent receives a single unit of fiat money. This is the Equal Incomes part of CEEI. * The agents trade freely until the market attains a Competitive Equilibrium. This is a price-vector and an allocation, such that (a) each allocated bundle is optimal to its agent given his/her income - the agent cannot purchase a better bundle with the same income, and (b) the market clears - the sum of all allocations exactly equals the initial endowment. The equilibrium allocation is provably envy free and Pareto efficient. Moreover, when the agents have linear utility functions, the CEEI allocation can be computed efficiently. Unfortunate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PPAD-hard
In computer science, PPAD ("Polynomial Parity Arguments on Directed graphs") is a complexity class introduced by Christos Papadimitriou in 1994. PPAD is a subclass of TFNP based on functions that can be shown to be total by a parity argument. The class attracted significant attention in the field of algorithmic game theory because it contains the problem of computing a Nash equilibrium: this problem was shown to be complete for PPAD by Daskalakis, Goldberg and Papadimitriou with at least 3 players and later extended by Chen and Deng to 2 players.*. Definition PPAD is a subset of the class TFNP, the class of function problems in FNP that are guaranteed to be total. The TFNP formal definition is given as follows: :A binary relation P(''x'',''y'') is in TFNP if and only if there is a deterministic polynomial time algorithm that can determine whether P(''x'',''y'') holds given both ''x'' and ''y'', and for every ''x'', there exists a ''y'' such that P(''x'',''y'') holds. Subclasses ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strongly Polynomial Time
In computer science, a ''polynomial-time algorithm'' is generally speaking an algorithm whose running time is upper-bounded by some polynomial function of the input size. The definition naturally depends on the computational model, which determines how the ''running time'' is measured, and how the ''input size'' is measured. Two prominent computational models are the Turing-machine model and the arithmetic model. A strongly-polynomial time algorithm is polynomial in both models, whereas a weakly-polynomial time algorithm is polynomial only in the Turing machine model. The difference between strongly- and weakly-polynomial time is when the inputs to the algorithms consist of integer or rational numbers. It is particularly common in optimization. Computational models Two common computational models are the Turing-machine model and the arithmetic model: * In the arithmetic model, every real number requires a single memory cell, whereas in the Turing model the storage size o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vijay Vazirani
Vijay Virkumar Vazirani (; b. 1957) is an Indian American distinguished professor of computer science in the Donald Bren School of Information and Computer Sciences at the University of California, Irvine. Education and career Vazirani first majored in electrical engineering at Indian Institute of Technology, Delhi but in his second year he transferred to MIT and received his bachelor's degree in computer science from MIT in 1979 and his Ph.D. from the University of California, Berkeley in 1983. His dissertation, ''Maximum Matchings without Blossoms'', was supervised by Manuel Blum. After postdoctoral research with Michael O. Rabin and Leslie Valiant at Harvard University, he joined the faculty at Cornell University in 1984. He moved to the IIT Delhi as a full professor in 1990, and moved again to the Georgia Institute of Technology in 1995. He was also a McKay Visiting Professor at the University of California, Berkeley, and a Distinguished SISL Visitor at the Social and Info ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irving Fisher
Irving Fisher (February 27, 1867 – April 29, 1947) was an American economist, statistician, inventor, eugenicist and progressive social campaigner. He was one of the earliest American neoclassical economists, though his later work on debt deflation has been embraced by the post-Keynesian school. Joseph Schumpeter described him as "the greatest economist the United States has ever produced", an assessment later repeated by James Tobin and Milton Friedman.Milton Friedman, ''Money Mischief: Episodes in Monetary History'', Houghton Mifflin Harcourt (1994) p. 37. Fisher made important contributions to utility theory and general equilibrium. He was also a pioneer in the rigorous study of intertemporal choice in markets, which led him to develop a theory of capital and interest rates. His research on the quantity theory of money inaugurated the school of macroeconomic thought known as "monetarism". Fisher was also a pioneer of econometrics, including the development of ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Market Equilibrium Computation
Market equilibrium computation (also called competitive equilibrium computation or clearing-prices computation) is a computational problem in the intersection of economics and computer science. The input to this problem is a ''market'', consisting of a set of ''resources'' and a set of ''agents''. There are various kinds of markets, such as Fisher market and Arrow–Debreu market, with divisible or indivisible resources. The required output is a ''competitive equilibrium'', consisting of a ''price-vector'' (a price for each resource), and an ''allocation'' (a resource-bundle for each agent), such that each agent gets the best bundle possible (for him) given the budget, and the market ''clears'' (all resources are allocated). Market equilibrium computation is interesting due to the fact that a competitive equilibrium is always Pareto efficient. The special case of a Fisher market, in which all buyers have equal incomes, is particularly interesting, since in this setting a competiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
