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Incentive Compatibility
In game theory and economics, a mechanism is called incentive-compatible (IC) if every participant can achieve their own best outcome by reporting their true preferences. For example, there is incentive compatibility if high-risk clients are better off in identifying themselves as high-risk to insurance firms, who only sell discounted insurance to high-risk clients. Likewise, they would be worse off if they pretend to be low-risk. Low-risk clients who pretend to be high-risk would also be worse off. The concept is attributed to the Russian-born American economist Leonid Hurwicz. Typology There are several different degrees of incentive-compatibility: * The stronger degree is dominant-strategy incentive-compatibility (DSIC). This 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 tru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions. It has applications in many fields of social science, and is used extensively in economics, logic, systems science and computer science. Initially, game theory addressed two-person zero-sum games, in which a participant's gains or losses are exactly balanced by the losses and gains of the other participant. In the 1950s, it was extended to the study of non zero-sum games, and was eventually applied to a wide range of Human behavior, behavioral relations. It is now an umbrella term for the science of rational Decision-making, decision making in humans, animals, and computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum games and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathematical economics. His paper was f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ranked Voting
Ranked voting is any voting system that uses voters' Ordinal utility, rankings of candidates to choose a single winner or multiple winners. More formally, a ranked vote system depends only on voters' total order, order of preference of the candidates. Ranked voting systems vary dramatically in how preferences are tabulated and counted, which gives them Comparison of voting rules, very different properties. In instant-runoff voting (IRV) and the single transferable vote system (STV), lower preferences are used as contingencies (back-up preferences) and are only applied when all higher-ranked preferences on a ballot have been eliminated or when the vote has been cast for a candidate who has been elected and surplus votes need to be transferred. Ranked votes of this type do not suffer the problem that a marked lower preference may be used against a voter's higher marked preference. Some ranked vote systems use ranks as weights; these systems are called positional voting. In the B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotonicity (mechanism Design)
In mechanism design, monotonicity is a property of a social choice function. It is a necessary condition for being able to implement such a function using a strategyproof mechanism. Its verbal description is: In other words: 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 assigns to each alternative. The vector of all value-functions is denoted by v. For every agent i, the vector of all value-functions of the ''other'' agents is denoted by v_. So v \equiv (v_i,v_). A social choice function is a function that takes as input the value-vector v and returns an outcome x\in X. It is denoted by \text(v) or \text(v_i,v_). In mechanisms without money A social choice function satisfies the strong monotonicity property (SMON) if for every agent i and every v_i,v_i',v_, if:x = \text(v_i, v_)x' = \text(v' ... [...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 good (economics), 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 Economic efficiency, 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 incidence, 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.0 . Existence Duncan K. Foley, Foley proved that, If the utility functions have continuous derivati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Implementability (mechanism Design)
Implementation theory is an area of research in game theory concerned with whether a class of Mechanism design, mechanisms (or institutions) can be designed whose equilibrium outcomes implement a given set of normative goals or Welfare economics, welfare criteria.Palfrey, Thomas R. "Chapter 61 Implementation Theory." Handbook of Game Theory with Economic Applications, 2002. . There are two general types of implementation problems: the economic problem of Production (economics), producing and Resource allocation, allocating Public good (economics), public and private goods and choosing over a finite set of alternatives.Maskin, Eric and Sjöström, Tomas. "Implementation Theory." Handbook of Social Choice and Welfare, 2002. . In the case of producing and allocating public/private goods, solution concepts are focused on finding Dominant Strategy, dominant strategies. In his paper "Counterspeculation, Auctions, and Competitive Sealed Tenders", William Vickrey showed that if preferences ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Game
In game theory, a Bayesian game is a strategic decision-making model which assumes players have incomplete information. Players may hold private information relevant to the game, meaning that the payoffs are not common knowledge. Bayesian games model the outcome of player interactions using aspects of Bayesian probability. They are notable because they allowed the specification of the solutions to games with incomplete information for the first time in game theory. Hungarian economist John C. Harsanyi introduced the concept of Bayesian games in three papers from 1967 and 1968: He was awarded the Nobel Memorial Prize in Economic Sciences for these and other contributions to game theory in 1994. Roughly speaking, Harsanyi defined Bayesian games in the following way: players are assigned a set of characteristics by nature at the start of the game. By mapping probability distributions to these characteristics and by calculating the outcome of the game using Bayesian probability, the r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean, mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is obtained through arithmetic, the expected value sometimes may not even be included in the sample data set; it is not the value you would expect to get in reality. 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 Integral, 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 a ... [...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] |
Gibbard–Satterthwaite Theorem
The Gibbard–Satterthwaite theorem is a theorem in social choice theory. It was first conjectured by the philosopher Michael Dummett and the mathematician Robin Farquharson in 1961 and then proved independently by the philosopher Allan Gibbard in 1973 and economist Mark Satterthwaite in 1975. It deals with deterministic ordinal electoral systems that choose a single winner, and shows that for every voting rule of this form, at least one of the following three things must hold: # The rule is dictatorial, i.e. there exists a distinguished voter who can choose the winner; or # The rule limits the possible outcomes to two alternatives only; or # The rule is not straightforward, i.e. there is no single always-best strategy (one that does not depend on other voters' preferences or behavior). Gibbard's proof of the theorem is more general and covers processes of collective decision that may not be ordinal, such as cardinal voting. Gibbard's 1978 theorem and Hylland's theorem are e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Majority Rule
In social choice theory, the majority rule (MR) is a social choice rule which says that, when comparing two options (such as bills or candidates), the option preferred by more than half of the voters (a ''majority'') should win. In political philosophy, the ''majority rule'' is one of two major competing notions of democracy. The most common alternative is given by the utilitarian rule (or other welfarist rules), which identify the spirit of liberal democracy with the equal consideration of interests.Ball, Terence and Antis Loizides"James Mill" The Stanford Encyclopedia of Philosophy (Winter 2020 Edition), Edward N. Zalta (ed.). Although the two rules can disagree in theory, political philosophers beginning with James Mill have argued the two can be reconciled in practice, with majority rule being a valid approximation to the utilitarian rule whenever voters share similarly-strong preferences. This position has found strong support in many social choice models, where the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economics
Economics () is a behavioral science that studies the Production (economics), production, distribution (economics), distribution, and Consumption (economics), consumption of goods and services. Economics focuses on the behaviour and interactions of Agent (economics), economic agents and how economy, economies work. Microeconomics analyses what is viewed as basic elements within economy, economies, including individual agents and market (economics), markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers. Macroeconomics analyses economies as systems where production, distribution, consumption, savings, and Expenditure, investment expenditure interact; and the factors of production affecting them, such as: Labour (human activity), labour, Capital (economics), capital, Land (economics), land, and Entrepreneurship, enterprise, inflation, economic growth, and public policies that impact gloss ... [...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] |
