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Incentive Compatibility
A mechanism is called incentive-compatible (IC) if every participant can achieve the best outcome to themselves just by acting according to their true preferences. There are several different degrees of incentive-compatibility: * The stronger degree is dominant-strategy incentive-compatibility (DSIC). It means that truth-telling is a weakly-dominant strategy, i.e. you fare best or at least not worse by being truthful, regardless of what the others do. In a DSIC mechanism, strategic considerations cannot help any agent achieve better outcomes than the truth; hence, such mechanisms are also called strategyproof or truthful. (See Strategyproofness) * A weaker degree is Bayesian-Nash incentive-compatibility (BNIC). It means that there is a Bayesian Nash equilibrium in which all participants reveal their true preferences. I.e, ''if'' all the others act truthfully, ''then'' it is also best or at least not worse for you to be truthful. Every DSIC mechanism is also BNIC, but a BNIC me ... [...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] |
Dominant Strategy
In game theory, strategic dominance (commonly called simply dominance) occurs when one strategy is better than another strategy for one player, no matter how that player's opponents may play. Many simple games can be solved using dominance. The opposite, intransitivity, occurs in games where one strategy may be better or worse than another strategy for one player, depending on how the player's opponents may play. Terminology When a player tries to choose the "best" strategy among a multitude of options, that player may compare two strategies A and B to see which one is better. The result of the comparison is one of: * B is equivalent to A: choosing B always gives the same outcome as choosing A, no matter what the other players do. * B strictly dominates A: choosing B always gives a better outcome than choosing A, no matter what the other players do. * B weakly dominates A: choosing B always gives at least as good an outcome as choosing A, no matter what the other players do, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strategyproofness
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, second- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Nash Equilibrium
In game theory, a Bayesian game is a game that models the outcome of player interactions using aspects of Bayesian probability. Bayesian games are notable because they allowed, for the first time in game theory, for the specification of the solutions to games with incomplete information. Hungarian economist John C. Harsanyi introduced the concept of Bayesian games in three papers from 1967 and 1968: He was awarded the Nobel Prize for these and other contributions to game theory in 1994. Roughly speaking, Harsanyi defined Bayesian games in the following way: players are assigned by nature at the start of the game a set of characteristics. By mapping probability distributions to these characteristics and by calculating the outcome of the game using Bayesian probability, the result is a game whose solution is, for technical reasons, far easier to calculate than a similar game in a non-Bayesian context. For those technical reasons, see the Specification of games section in this article ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Majority Voting
Majority rule is a principle that means the decision-making power belongs to the group that has the most members. In politics, majority rule requires the deciding vote to have majority, that is, more than half the votes. It is the binary decision rule used most often in influential decision-making bodies, including many legislatures of democratic nations. Distinction with plurality Decision-making in a legislature is different from election of representation, although the result of plurality (First Past the Post or FPTP) elections is often mistaken for majority rule. Plurality elections elect the option that has more votes than any other, regardless of whether the fifty percent threshold is passed. A plurality election produces representation of a majority when there are only two candidates in an election or, more generally, when there are only two options. However, when there are more than two alternatives, a candidate that has less than fifty percent of the votes cast in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second-price Auction
A Vickrey auction or sealed-bid second-price auction (SBSPA) is a type of sealed-bid auction. Bidders submit written bids without knowing the bid of the other people in the auction. The highest bidder wins but the price paid is the second-highest bid. This type of auction is strategically similar to an English auction and gives bidders an incentive to bid their true value. The auction was first described academically by Columbia University professor William Vickrey in 1961 though it had been used by stamp collectors since 1893. In 1797 Johann Wolfgang von Goethe sold a manuscript using a sealed-bid, second-price auction. Vickrey's original paper mainly considered auctions where only a single, indivisible good is being sold. The terms ''Vickrey auction'' and ''second-price sealed-bid auction'' are, in this case only, equivalent and used interchangeably. In the case of multiple identical goods, the bidders submit inverse demand curves and pay the opportunity cost. Vickrey auctions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plurality Voting
Plurality voting refers to electoral systems in which a candidate, or candidates, who poll more than any other counterpart (that is, receive a plurality), are elected. In systems based on single-member districts, it elects just one member per district and may also be referred to as first-past-the-post (FPTP), single-member plurality (SMP/SMDP), single-choice voting (an imprecise term as non-plurality voting systems may also use a single choice), simple plurality or relative majority (as opposed to an ''absolute majorit''y, where more than half of votes is needed, this is called ''majority voting''). A system which elects multiple winners elected at once with the plurality rule, such as one based on multi-seat districts, is referred to as plurality block voting. Plurality voting is distinguished from ''majority voting'', in which a winning candidate must receive an absolute majority of votes: more than half of all votes (more than all other candidates combined if each voter ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-price Auction
A first-price sealed-bid auction (FPSBA) is a common type of auction. It is also known as blind auction. In this type of auction, all bidders simultaneously submit sealed bids so that no bidder knows the bid of any other participant. The highest bidder pays the price that was submitted. Strategic analysis In a FPSBA, each bidder is characterized by their monetary valuation of the item for sale. Suppose Alice is a bidder and her valuation is a. Then, if Alice is rational: *She will never bid more than a, because bidding more than a can only make her lose net value. *If she bids exactly a, then she will not lose but also not gain any positive value. *If she bids less than a, then she ''may'' have some positive gain, but the exact gain depends on the bids of the others. Alice would like to bid the smallest amount that can make her win the item, as long as this amount is less than a. For example, if there is another bidder Bob and he bids y and y [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with also often stylized as or \mathbb. History The idea of the expected value originated in the middle of the 17th century from the study of the so-called problem of points, which seeks to divide the stakes ''in a fair way'' between two players, who have to end th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Game
In game theory, a Bayesian game is a game that models the outcome of player interactions using aspects of Bayesian probability. Bayesian games are notable because they allowed, for the first time in game theory, for the specification of the solutions to games with incomplete information. Hungarian economist John C. Harsanyi introduced the concept of Bayesian games in three papers from 1967 and 1968: He was awarded the Nobel Prize for these and other contributions to game theory in 1994. Roughly speaking, Harsanyi defined Bayesian games in the following way: players are assigned by nature at the start of the game a set of characteristics. By mapping probability distributions to these characteristics and by calculating the outcome of the game using Bayesian probability, the result is a game whose solution is, for technical reasons, far easier to calculate than a similar game in a non-Bayesian context. For those technical reasons, see the Specification of games section in this article ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Implementability (mechanism Design)
In mechanism design, implementability is a property of a social choice function. It means that there is an incentive-compatible mechanism that attains ("implements") this function. There are several degrees of implementability, corresponding to the different degrees of incentive-compatibility, e.g: * A function is dominant-strategy implementable if it is attainable by a mechanism which is dominant-strategy-incentive-compatible (also called strategyproof 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 ...). * A function is Bayesian-Nash implementable if it is attainable by a mechanism which is Bayesian-Nash-incentive-compatible. See for a recent reference. In some textbooks, the entire field of mechanism design is called Implementation theory.Martin J. Osborne & Ariel Rubinstein: A Cour ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lindahl Tax
A Lindahl tax is a form of taxation conceived by Erik Lindahl in which individuals pay for public goods according to their marginal benefits. In other words, they pay according to the amount of satisfaction or utility they derive from the consumption of an additional unit of the public good. Lindahl taxation is designed to maximize efficiency for each individual and provide the optimal level of a public good. Lindahl taxes can be seen as an individual's share of the collective tax burden of an economy. The optimal level of a public good is that quantity at which the willingness to pay for one more unit of the good, taken in totality for all the individuals is equal to the marginal cost of supplying that good. Lindahl tax is the optimal quantity times the willingness to pay for one more unit of that good at this quantity. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
