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Straightforwardness
In mechanism design, a strategyproof (SP) mechanism is a game form in which each player has a weakly-dominant strategy, so that no player can gain by "spying" over the other players to know what they are going to play. When the players have private information (e.g. their type or their value to some item), and the strategy space of each player consists of the possible information values (e.g. possible types or values), a truthful mechanism is a game in which revealing the true information is a weakly-dominant strategy for each player. An SP mechanism is also called dominant-strategy-incentive-compatible (DSIC), to distinguish it from other kinds of incentive compatibility. A SP mechanism is immune to manipulations by individual players (but not by coalitions). In contrast, in a group strategyproof mechanism, no group of people can collude to misreport their preferences in a way that makes every member better off. In a strong group strategyproof mechanism, no group of people can col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbard's Theorem
In the fields of mechanism design and social choice theory, Gibbard's theorem is a result proven by philosopher Allan Gibbard in 1973. It states that for any deterministic process of collective decision, at least one of the following three properties must hold: # The process is Dictatorship mechanism, dictatorial, i.e. there is a single voter whose vote chooses the outcome. # The process limits the possible outcomes to two options only. # The process is not straightforward; the optimal ballot for a voter "requires strategic voting", i.e. it depends on their beliefs about other voters' ballots. A corollary of this theorem is the Gibbard–Satterthwaite theorem about voting rules. The key difference between the two theorems is that Gibbard–Satterthwaite applies only to ranked voting. Because of its broader scope, Gibbard's theorem makes no claim about whether voters need to reverse their ranking of candidates, only that their optimal ballots depend on the other voters' ballots. Gib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dominant Strategy
In game theory, a strategy ''A'' dominates another strategy ''B'' if ''A'' will always produce a better result than ''B'', regardless of how any other player plays. Some very simple games (called straightforward games) can be solved using dominance. Terminology A player can compare two strategies, A and B, to determine which one is better. The result of the comparison is one of: * 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, and there is at least one set of opponents' actions for which B gives a better outcome than A. (Notice that if B strictly dominates A, then B weakly dominates A. Therefore, we can say "B dominates A" to mean "B weakly dominates A".) * B is weakly dominated by A: there is at least one set of opponents' actions for which B gives a worse outcome than A, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Form
In game theory and related fields, a game form, game frame, ruleset, or outcome function is the set of rules that govern a game and determine its outcome based on each player's choices. A game form differs from a game in that it does not stipulate the utilities or payoffs for each agent. Mathematically, a game form can be defined as a mapping going from an ''action'' ''space''—which describes all the possible moves a player can make— to an ''outcome space''. The action space is also often called a ''message space'' when the actions consist of providing information about beliefs or preferences, in which case it is called a direct mechanism. For example, an electoral system is a game form mapping a message space consisting of ballots to a winning candidate (the outcome). Similarly, an auction is a game form that takes each bidder's price and maps them to both a winner and a set of payments by the bidders. Often, a game form is a set of rules or institutions designed to implem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mechanism Design
Mechanism design (sometimes implementation theory or institution design) is a branch of economics and game theory. It studies how to construct rules—called Game form, mechanisms or institutions—that produce good outcomes according to Social welfare function, some predefined metric, even when the designer does not know the players' true preferences or what information they have. Mechanism design thus focuses on the study of solution concepts for a class of private-information games. Mechanism design has broad applications, including traditional domains of economics such as market design, but also political science (through voting theory). It is a foundational component in the operation of the internet, being used in networked systems (such as inter-domain routing), e-commerce, and Sponsored search auction, advertisement auctions by Facebook and Google. Because it starts with the end of the game (a particular result), then works backwards to find a game that implements it, it ... [...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] |
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] |
Participation Criterion
The participation criterion is a voting system criterion that says candidates should never lose an election as a result of receiving too many votes in support. More formally, it says that adding more voters who prefer ''Alice'' to ''Bob'' should not cause ''Alice'' to lose the election to ''Bob''. Voting systems that fail the participation criterion exhibit the no-show paradox, where a voter is effectively disenfranchised by the electoral system because turning out to vote could make the result worse for them; such voters are sometimes referred to as having negative vote weights, particularly in the context of German constitutional law, where courts have ruled such a possibility violates the principle of one man, one vote. Positional methods and score voting satisfy the participation criterion. All deterministic voting rules that satisfy pairwise majority-rule can fail in situations involving four-way cyclic ties, though such scenarios are empirically rare, and the random ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Individual Rationality
Rational choice modeling refers to the use of decision theory (the theory of rational choice) as a set of guidelines to help understand economic and social behavior. The theory tries to approximate, predict, or mathematically model human behavior by analyzing the behavior of a rational actor facing the same costs and benefits.Gary Browning, Abigail Halcli, Frank Webster (2000). ''Understanding Contemporary Society: Theories of the Present'', London: Sage Publications. Rational choice models are most closely associated with economics, where mathematical analysis of behavior is standard. However, they are widely used throughout the social sciences, and are commonly applied to cognitive science, criminology, political science, and sociology. Overview The basic premise of rational choice theory is that the decisions made by individual actors will collectively produce aggregate social behaviour. The theory also assumes that individuals have preferences out of available choice ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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] |
Consensus Estimate
Consensus estimate is a technique for designing truthful mechanisms in a prior-free mechanism design setting. The technique was introduced for digital goods auctions and later extended to more general settings. Suppose there is a digital good that we want to sell to a group of buyers with unknown valuations. We want to determine the price that will bring us maximum profit. Suppose we have a function that, given the valuations of the buyers, tells us the maximum profit that we can make. We can use it in the following way: # Ask the buyers to tell their valuations. # Calculate R_ - the maximum profit possible given the valuations. # Calculate a price that guarantees that we get a profit of R_. Step 3 can be attained by a profit extraction mechanism, which is a truthful mechanism In mechanism design, a strategyproof (SP) mechanism is a game form in which each player has a weakly- dominant strategy, so that no player can gain by "spying" over the other players to know what they are g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lexicographic Dominance
Lexicographic dominance is a total order between random variables. It is a form of stochastic ordering. It is defined as follows. Random variable A has lexicographic dominance over random variable B (denoted A \succ_ B) if one of the following holds: * A has a higher probability than B of receiving the best outcome. * A and B have an equal probability of receiving the best outcome, but A has a higher probability of receiving the 2nd-best outcome. * A and B have an equal probability of receiving the best and 2nd-best outcomes, but A has a higher probability of receiving the 3rd-best outcome. In other words: let ''k'' be the first index for which the probability of receiving the k-th best outcome is different for A and B. Then this probability should be higher for A. Variants Upward lexicographic dominance is defined as follows. Random variable A has upward lexicographic dominance over random variable B (denoted A \succ_ B) if one of the following holds: * A has a ''lower'' probabi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
