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Myerson Ironing
Mechanism design is a field in economics and game theory that takes an objectives-first approach to designing economic mechanisms or incentives, toward desired objectives, in strategic settings, where players act rationally. Because it starts at the end of the game, then goes backwards, it is also called reverse game theory. It has broad applications, from economics and politics in such fields as market design, auction theory and social choice theory to networked-systems (internet interdomain routing, sponsored search auctions). Mechanism design studies solution concepts for a class of private-information games. Leonid Hurwicz explains that 'in a design problem, the goal function is the main "given", while the mechanism is the unknown. Therefore, the design problem is the "inverse" of traditional economic theory, which is typically devoted to the analysis of the performance of a given mechanism.' So, two distinguishing features of these games are: * that a game "designer" choos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stanley Reiter MDdiagram
Stanley may refer to: Arts and entertainment Film and television * ''Stanley'' (1972 film), an American horror film * ''Stanley'' (1984 film), an Australian comedy * ''Stanley'' (1999 film), an animated short * ''Stanley'' (1956 TV series), an American situation comedy * ''Stanley'' (2001 TV series), an American animated series Other uses in arts and entertainment * ''Stanley'' (play), by Pam Gems, 1996 * Stanley Award, an Australian Cartoonists' Association award * '' Stanley: The Search for Dr. Livingston'', a video game * Stanley (Cars), a character in ''Cars Toons: Mater's Tall Tales'' * ''The Stanley Parable'', a 2011 video game developed by Galactic Cafe, and its titular character, Stanley Businesses and organisations * Stanley, Inc., American information technology company * Stanley Aviation, American aerospace company * Stanley Black & Decker, formerly The Stanley Works, American hardware manufacturer ** Stanley knife, a utility knife * Stanley bottle, a br ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanism Design
Mechanism design is a field in economics and game theory that takes an objectives-first approach to designing economic mechanisms or incentives, toward desired objectives, in strategic settings, where players act rationally. Because it starts at the end of the game, then goes backwards, it is also called reverse game theory. It has broad applications, from economics and politics in such fields as market design, auction theory and social choice theory to networked-systems (internet interdomain routing, sponsored search auctions). Mechanism design studies solution concepts for a class of private-information games. Leonid Hurwicz explains that 'in a design problem, the goal function is the main "given", while the mechanism is the unknown. Therefore, the design problem is the "inverse" of traditional economic theory, which is typically devoted to the analysis of the performance of a given mechanism.' So, two distinguishing features of these games are: * that a game "designer" choos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hazard Rate
Survival analysis is a branch of statistics for analyzing the expected duration of time until one event occurs, such as death in biological organisms and failure in mechanical systems. This topic is called reliability theory or reliability analysis in engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ..., duration analysis or duration modelling in economics, and event history analysis in sociology. Survival analysis attempts to answer certain questions, such as what is the proportion of a population which will survive past a certain time? Of those that survive, at what rate will they die or fail? Can multiple causes of death or failure be taken into account? How do particular circumstances or characteristics increase or decrease the probability of survival? To answer such q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Envelope Theorem
In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization problem. As we change parameters of the objective, the envelope theorem shows that, in a certain sense, changes in the optimizer of the objective do not contribute to the change in the objective function. The envelope theorem is an important tool for comparative statics of optimization models. The term envelope derives from describing the graph of the value function as the "upper envelope" of the graphs of the parameterized family of functions \left\ _ that are optimized. Statement Let f(x,\alpha) and g_(x,\alpha), j = 1,2, \ldots, m be real-valued continuously differentiable functions on \mathbb^, where x \in \mathbb^ are choice variables and \alpha \in \mathbb^ are parameters, and consider the problem of choosing x, for a given \alpha, so as to: : \max_ f(x, \alpha) subject to g_(x,\alpha) \geq 0, j = 1,2, \ldots, m an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulative Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an ''upwards continuous'' ''monotonic increasing'' cumulative distribution function F : \mathbb R \rightarrow ,1/math> satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability that the random variable X takes on a value less tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quasilinear Utility
In economics and consumer theory, quasilinear utility functions are linear in one argument, generally the numeraire. Quasilinear preferences can be represented by the utility function u(x_1, x_2, \ldots, x_n) = x_1 + \theta (x_2, \ldots, x_n) where \theta is strictly concave. A useful property of the quasilinear utility function is that the Marshallian/Walrasian demand for x_2, \ldots, x_n does not depend on wealth and is thus not subject to a wealth effect; The absence of a wealth effect simplifies analysis and makes quasilinear utility functions a common choice for modelling. Furthermore, when utility is quasilinear, compensating variation (CV), equivalent variation (EV), and consumer surplus are algebraically equivalent. In mechanism design, quasilinear utility ensures that agents can compensate each other with side payments. Definition in terms of preferences A preference relation \succsim is quasilinear with respect to commodity 1 (called, in this case, the ''numeraire'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Price Of Stability
In game theory, the price of stability (PoS) of a game is the ratio between the best objective function value of one of its equilibria and that of an optimal outcome. The PoS is relevant for games in which there is some objective authority that can influence the players a bit, and maybe help them converge to a good Nash equilibrium. When measuring how efficient a Nash equilibrium is in a specific game we often also talk about the price of anarchy (PoA), which is the ratio between the ''worst'' objective function value of one of its equilibria and that of an optimal outcome. Examples Another way of expressing PoS is: : \text = \frac ,\ \text \geq 0. In particular, if the optimal solution is a Nash equilibrium, then the PoS is 1. In the following prisoner’s dilemma game, since there is a single equilibrium (B,R) we have PoS = PoA = 1/2. On this example which is a version of the battle of sexes game, there are two equilibrium points, (T,L) and (B,R), with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Price Of Anarchy
The Price of Anarchy (PoA) is a concept in economics and game theory that measures how the efficiency of a system degrades due to selfish behavior of its agents. It is a general notion that can be extended to diverse systems and notions of efficiency. For example, consider the system of transportation of a city and many agents trying to go from some initial location to a destination. Let efficiency in this case mean the average time for an agent to reach the destination. In the 'centralized' solution, a central authority can tell each agent which path to take in order to minimize the average travel time. In the 'decentralized' version, each agent chooses its own path. The Price of Anarchy measures the ratio between average travel time in the two cases. Usually the system is modeled as a game and the efficiency is some function of the outcomes (e.g. maximum delay in a network, congestion in a transportation system, social welfare in an auction, etc.). Different concepts of equilibriu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fundamental Theorems Of Welfare Economics
There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information, and in perfect competition, will be Pareto optimal (in the sense that no further exchange would make one person better off without making another worse off). The requirements for perfect competition are these: # There are no externalities and each actor has perfect information. # Firms and consumers take prices as given (no economic actor or group of actors has market power). The theorem is sometimes seen as an analytical confirmation of Adam Smith's "invisible hand" principle, namely that ''competitive markets ensure an efficient allocation of resources''. However, there is no guarantee that the Pareto optimal market outcome is socially desirable, as there are many possible Pareto efficient allocations of resources differing in their desirability (e.g. one person may own everything and everyone else nothing). The second th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arrow's Impossibility Theorem
Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states that when voters have three or more distinct alternatives (options), no ranked voting electoral system can convert the ranked preferences of individuals into a community-wide (complete and transitive) ranking while also meeting the specified set of criteria: '' unrestricted domain'', '' non-dictatorship'', ''Pareto efficiency'', and ''independence of irrelevant alternatives''. The theorem is often cited in discussions of voting theory as it is further interpreted by the Gibbard–Satterthwaite theorem. The theorem is named after economist and Nobel laureate Kenneth Arrow, who demonstrated the theorem in his doctoral thesis and popularized it in his 1951 book ''Social Choice and Individual Values''. The original paper was titled "A Difficulty in the Concept of Social Welfare". In short, the theorem states that no rank-order electoral syst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tragedy Of The Commons
Tragedy (from the grc-gre, τραγῳδία, ''tragōidia'', ''tragōidia'') is a genre of drama based on human suffering and, mainly, the terrible or sorrowful events that befall a main character. Traditionally, the intention of tragedy is to invoke an accompanying catharsis, or a "pain hatawakens pleasure", for the audience. While many cultures have developed forms that provoke this paradoxical response, the term ''tragedy'' often refers to a specific tradition of drama that has played a unique and important role historically in the self-definition of Western civilization. That tradition has been multiple and discontinuous, yet the term has often been used to invoke a powerful effect of cultural identity and historical continuity—"the Greeks and the Elizabethans, in one cultural form; Hellenes and Christians, in a common activity," as Raymond Williams puts it. From its origins in the theatre of ancient Greece 2500 years ago, from which there survives only a fraction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Distribution
In probability theory and statistics, a probability distribution is the mathematical Function (mathematics), function that gives the probabilities of occurrence of different possible outcomes for an Experiment (probability theory), experiment. It is a mathematical description of a Randomness, random phenomenon in terms of its sample space and the Probability, probabilities of Event (probability theory), events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that fair coin, the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a Survey methodology, survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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