Market Design
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Market Design
Market design is a practical methodology for creation of markets of certain properties, which is partially based on mechanism design. In some markets, prices may be used to induce the desired outcomes — these markets are the study of auction theory. In other markets, prices may not be used — these markets are the study of matching theory. In his 2008, Nemmers Prize lecture, Market Design and Stanford University economist Paul Milgrom commented on the interdisciplinary nature of market design: "Market design is a kind of economic engineering, utilizing laboratory research, game theory, algorithms, simulations, and more. Its challenges inspire us to rethink longstanding fundamentals of economic theory."Milgrom Nemmers Prize Presentation Slides, 2008
Milgrom is, along with ...
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Paul Milgrom
Paul Robert Milgrom (born April 20, 1948) is an American economist. He is the Shirley and Leonard Ely Professor of Humanities and Sciences at the Stanford University School of Humanities and Sciences, a position he has held since 1987. He is a professor in the Stanford School of Engineering as well and a Senior Fellow at the Stanford Institute for Economic Research. Milgrom is an expert in game theory, specifically auction theory and pricing strategies. He is the winner of the 2020 Nobel Memorial Prize in Economic Sciences, together with Robert B. Wilson, "for improvements to auction theory and inventions of new auction formats". He is the co-creator of the no-trade theorem with Nancy Stokey. He is the co-founder of several companies, the most recent of which, Auctionomics, provides software and services for commercial auctions and exchanges. Milgrom and his thesis advisor Wilson designed the auction protocol the FCC uses to determine which phone company gets what cellula ...
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David Gale
David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". was, according to the Hebrew Bible, the third king of the United Kingdom of Israel. In the Books of Samuel, he is described as a young shepherd and harpist who gains fame by slaying Goliath, a champion of the Philistines, in southern Canaan. David becomes a favourite of Saul, the first king of Israel; he also forges a notably close friendship with Jonathan, a son of Saul. However, under the paranoia that David is seeking to usurp the throne, Saul attempts to kill David, forcing the latter to go into hiding and effectively operate as a fugitive for several years. After Saul and Jonathan are both killed in battle against the Philistines, a 30-year-old David is anointed king over all of Israel and Judah. Following his rise to power, David c ...
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Mathematical And Quantitative Methods (economics)
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ...
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Economic Theories
Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes what's viewed as basic elements in the economy, including individual agents and markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers. Macroeconomics analyzes the economy as a system where production, consumption, saving, and investment interact, and factors affecting it: employment of the resources of labour, capital, and land, currency inflation, economic growth, and public policies that have impact on these elements. Other broad distinctions within economics include those between positive economics, describing "what is", and normative economics, advocating "what ought to be"; between economic theory and applied economics; between rational and ...
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Auction Theory
Auction theory is an applied branch of economics which deals with how bidders act in auction markets and researches how the features of auction markets Incentivisation, incentivise predictable outcomes. Auction theory is a tool used to inform the design of real-world auctions. Sellers use auction theory to raise higher revenues while allowing buyers to procure at a lower cost. The conference of the price between the buyer and seller is an economic equilibrium. Auction theorists design rules for auctions to address issues which can lead to market failure. The design of these rulesets encourages optimal bidding strategies among a variety of informational settings. The 2020 Nobel Prize for Economics was awarded to Paul R. Milgrom and Robert B. Wilson “for improvements to auction theory and inventions of new Auction#Types, auction formats.” Introduction Auctions facilitate transactions by enforcing a specific set of rules regarding the resource allocations of a group of bidders. T ...
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Designing Economic Mechanisms
''Designing Economic Mechanisms'' is a 2006 book by economists Leonid Hurwicz and Stanley Reiter. Hurwicz received the 2007 Nobel Memorial Prize in Economic Sciences with Eric Maskin and Roger Myerson for their work on mechanism design. In this book, Hurwicz and Reiter presented systematic methods for designing decentralized economic mechanisms whose performance attains specified goals. Summary The authors of this book, Leonid Hurwicz and Stanley Reiter, helped found the field of mechanism design. This book provides a guide for those who would design mechanisms. A decentralized mechanism is a mathematical structure that models institutions for guiding and coordinating economic activity. Such institution Institutions are humanly devised structures of rules and norms that shape and constrain individual behavior. All definitions of institutions generally entail that there is a level of persistence and continuity. Laws, rules, social conventions a ...s are usually created by a ...
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Doubly Stochastic Matrix
In mathematics, especially in probability and combinatorics, a doubly stochastic matrix (also called bistochastic matrix) is a square matrix X=(x_) of nonnegative real numbers, each of whose rows and columns sums to 1, i.e., :\sum_i x_=\sum_j x_=1, Thus, a doubly stochastic matrix is both left stochastic and right stochastic. Indeed, any matrix that is both left and right stochastic must be square: if every row sums to one then the sum of all entries in the matrix must be equal to the number of rows, and since the same holds for columns, the number of rows and columns must be equal. Birkhoff polytope The class of n\times n doubly stochastic matrices is a convex polytope known as the Birkhoff polytope B_n. Using the matrix entries as Cartesian coordinates, it lies in an (n-1)^2-dimensional affine subspace of n^2-dimensional Euclidean space defined by 2n-1 independent linear constraints specifying that the row and column sums all equal one. (There are 2n-1 constraints rather than ...
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Spectrum Auction
A spectrum auction is a process whereby a government uses an auction system to sell the rights to transmit signals over specific bands of the electromagnetic spectrum and to assign scarce spectrum resources. Depending on the specific auction format used, a spectrum auction can last from a single day to several months from the opening bid to the final winning bid. With a well-designed auction, resources are allocated efficiently to the parties that value them the most, the government securing revenue in the process. Spectrum auctions are a step toward market-based spectrum management and privatization of public airwaves, and are a way for governments to allocate scarce resources. Alternatives to auctions include administrative licensing, such as the comparative hearings conducted historically (sometimes referred to as "beauty contests"), or lotteries. Innovation In the past decade, telecommunications has turned into a highly competitive industry where companies are competing to ...
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Policy
Policy is a deliberate system of guidelines to guide decisions and achieve rational outcomes. A policy is a statement of intent and is implemented as a procedure or protocol. Policies are generally adopted by a governance body within an organization. Policies can assist in both ''subjective'' and ''objective'' decision making. Policies used in subjective decision-making usually assist senior management with decisions that must be based on the relative merits of a number of factors, and as a result, are often hard to test objectively, e.g. work–life balance policy... Moreover, Governments and other institutions have policies in the form of laws, regulations, procedures, administrative actions, incentives and voluntary practices. Frequently, resource allocations mirror policy decisions. In contrast, policies to assist in objective decision-making are usually operational in nature and can be objectively tested, e.g. password policy. The term may apply to government, public se ...
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Knaster–Tarski Theorem
In the mathematics, mathematical areas of order theory, order and lattice theory, the Knaster–Tarski theorem, named after Bronisław Knaster and Alfred Tarski, states the following: :''Let'' (''L'', ≤) ''be a complete lattice and let f : L → L be an Monotonic function#In order theory, monotonic function (w.r.t. ≤ ). Then the set (mathematics), set of fixed point (mathematics), fixed points of f in L also forms a complete lattice under ≤ .'' It was Tarski who stated the result in its most general form, and so the theorem is often known as Tarski's fixed-point theorem. Some time earlier, Knaster and Tarski established the result for the special case where ''L'' is the lattice (order), lattice of subsets of a set, the power set lattice. The theorem has important applications in formal semantics of programming languages and abstract interpretation. A kind of converse (logic), converse of this theorem was mathematical proof, proved by Anne C. Morel, Anne C. Davi ...
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Lattice (order)
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the power set of a set, partially ordered by inclusion, for which the supremum is the union and the infimum is the intersection. Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple and the infimum is the greatest common divisor. Lattices can also be characterized as algebraic structures satisfying certain axiomatic identities. Since the two definitions are equivalent, lattice theory draws on both order theory and universal algebra. Semilattices include lattices, which in turn include Heyting and Boolean algebras. These ''lattice-like'' structures all admi ...
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