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Implementation Theory
Implementation theory is an area of research in game theory concerned with whether a class of mechanisms (or institutions) can be designed whose equilibrium outcomes implement a given set of normative goals or 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 producing and allocating public and private goods and choosing over a finite set of alternatives.Maskin, Eric. "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 strategies. In his paper "Counterspeculation, Auctions, and Competitive Sealed Tenders", William Vickrey showed that if preferences are restricted to the case of quasi-linear utility functions then the mechanism dominant strategy is dominant-strategy implementable. "A social ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game 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 mathema ... [...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] |
Outcome (game Theory)
In game theory, an outcome is a situation which results from a combination of player's strategies. Formally, a path through the game tree, or equivalently a terminal node of the game tree. A primary purpose of game theory is to determine the outcomes of games according to a solution concept (e.g. Nash equilibrium). In a game where chance or a random event is involved, the outcome is not known from only the set of strategies, but is only realized when the random event(s) are realized. A set of payoffs can be considered a set of N-tuples, where ''N'' is the number of players in the game, and the cardinality of the set is equal to the total number of possible outcomes when the strategies of the players are varied. The payoff set can thus be partially ordered, where the partial ordering comes from the value of each entry in the N-tuple. How players interact to allocate the payoffs among themselves is a fundamental aspect of economics. Choosing among outcomes Many different concep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Revelation Mechanism
The revelation principle is a fundamental principle in mechanism design. It states that if a social choice function can be implemented by an arbitrary mechanism (i.e. if that mechanism has an equilibrium outcome that corresponds to the outcome of the social choice function), then the same function can be implemented by an incentive-compatible-direct-mechanism (i.e. in which players truthfully report type) with the same equilibrium outcome (payoffs). In mechanism design, the revelation principle is of utmost importance in finding solutions. The researcher need only look at the set of equilibria characterized by incentive compatibility. That is, if the mechanism designer wants to implement some outcome or property, they can restrict their search to mechanisms in which agents are willing to reveal their private information to the mechanism designer that has that outcome or property. If no such direct and truthful mechanism exists, no mechanism can implement this outcome/property b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Strategy Proof
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] |
Incentive Compatible
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 mech ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Choice
Social choice theory or social choice is a theoretical framework for analysis of combining individual opinions, preferences, interests, or welfares to reach a ''collective decision'' or ''social welfare'' in some sense.Amartya Sen (2008). "Social Choice,". ''The New Palgrave Dictionary of Economics'', 2nd EditionAbstract & TOC./ref> Whereas choice theory is concerned with individuals making choices based on their preferences, social choice theory is concerned with how to translate the preferences of individuals into the preferences of a group. A non-theoretical example of a collective decision is enacting a law or set of laws under a constitution. Another example is voting, where individual preferences over candidates are collected to elect a person that best represents the group's preferences. Social choice blends elements of welfare economics and public choice theory. It is methodologically individualistic, in that it aggregates preferences and behaviors of individual member ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Vickrey
William Spencer Vickrey (21 June 1914 – 11 October 1996) was a Canadian-American professor of economics and Nobel Laureate. Vickrey was awarded the 1996 Nobel Memorial Prize in Economic Sciences with James Mirrlees for their research into the economic theory of incentives under asymmetric information, becoming the only Nobel laureate born in British Columbia. The announcement of his Nobel Prize was made just three days prior to his death. Vickrey died while traveling to a conference of Georgist academics that he helped found and never missed once in 20 years. His Columbia University economics department colleague C. Lowell Harriss accepted the posthumous prize on his behalf. There are only three other cases where a Nobel Prize has been presented posthumously. Early years Vickrey was born in Victoria, British Columbia and attended high school at Phillips Academy in Andover, Massachusetts. After obtaining his B.S. in Mathematics at Yale University in 1935, he went on to comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solution Concept
In game theory, a solution concept is a formal rule for predicting how a game will be played. These predictions are called "solutions", and describe which strategies will be adopted by players and, therefore, the result of the game. The most commonly used solution concepts are equilibrium concepts, most famously Nash equilibrium. Many solution concepts, for many games, will result in more than one solution. This puts any one of the solutions in doubt, so a game theorist may apply a refinement to narrow down the solutions. Each successive solution concept presented in the following improves on its predecessor by eliminating implausible equilibria in richer games. Formal definition Let \Gamma be the class of all games and, for each game G \in \Gamma, let S_G be the set of strategy profiles of G. A ''solution concept'' is an element of the direct product \Pi_2^; ''i.e''., a function F: \Gamma \rightarrow \bigcup\nolimits_ 2^ such that F(G) \subseteq S_G for all G \in \Gamma. Ra ... [...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] |
Private Good
A private good is defined in economics as "an item that yields positive benefits to people" that is excludable, i.e. its owners can exercise private property rights, preventing those who have not paid for it from using the good or consuming its benefits; and rivalrous, i.e. consumption by one necessarily prevents that of another. A private good, as an economic resource is scarce, which can cause competition for it. The market demand curve for a private good is a horizontal summation of individual demand curves. Unlike public goods, such as clean air or national defense, private goods are less likely to have the free rider problem, in which a person benefits from a public good without contributing towards it. Assuming a private good is valued positively by everyone, the efficiency of obtaining the good is obstructed by its rivalry; that is simultaneous consumption of a rivalrous good is theoretically impossible. The feasibility of obtaining the good is made difficult by its excludab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Public Good (economics)
In economics, a public good (also referred to as a social good or collective good)Oakland, W. H. (1987). Theory of public goods. In Handbook of public economics (Vol. 2, pp. 485-535). Elsevier. is a good that is both non-excludable and non-rivalrous. For such goods, users cannot be barred from accessing or using them for failing to pay for them. Also, use by one person neither prevents access of other people nor does it reduce availability to others. Therefore, the good can be used simultaneously by more than one person. This is in contrast to a common good, such as wild fish stocks in the ocean, which is non-excludable but rivalrous to a certain degree. If too many fish were harvested, the stocks would deplete, limiting the access of fish for others. A public good must be valuable to more than one user, otherwise, the fact that it can be used simultaneously by more than one person would be economically irrelevant. Capital goods may be used to produce public goods or services th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
