**Mechanism design** is a sub-field of game theory. It is the art of designing rules of a game to achieve a specific outcome. This is done by setting up a structure in which each player has an incentive to behave as the designer intends. The game is then said to implement the desired outcome. The strength of such a result depends on the solution concept used in the game. Game theory is a hybrid branch of applied mathematics and economics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ...
In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified. ...
Most of the results in mechanism design have been established by economists, but some mathematicians, computer scientists and electrical engineers also work in the field. An economist is an individual who studies, develops, and applies theories and concepts from economics, and writes about economic policy. ...
One branch of mechanism design is the creation of markets such as auctions. Another is the design of matching algorithms such as the one used to pair medical school graduates with internships. A third application is to the provison of public goods, and the optimal design of taxation schemes by governments. A market is, as defined in economics, a social arrangement that allows buyers and sellers to discover information and carry out a voluntary exchange. ...
An auctioneer and her assistants scan the crowd for bidders An auction is the process of buying and selling things by offering them up for bid, taking bids, and then selling the item to the highest bidder. ...
In economics, a public good is one that cannot or will not be produced for individual profit, since it is difficult to get people to pay for its large beneficial externalities. ...
A common exercise in mechanism design is to achieve the desired outcome according to a specific solution concept. The celebrated Gibbard-Satterthwaite theorem shows that any outcome that can be implemented as a dominant strategy equilibrium is necessarily dictatorial. This is similar to Arrow's Impossibility Theorem. By contrast, implementation in Nash equilibrium is possible for a much wider range of social choice rules. The Gibbard-Satterthwaite theorem is a result about voting systems designed to choose a single winner from the preferences of certain individuals, where each individual ranks all candidates in order of preference. ...
In game theory, dominance (also called strategic dominance) occurs when one strategy is better than another strategy for one player, no matter how that players opponents may play. ...
Dictator was the title of a magistrate in ancient Rome appointed by the Senate to rule the state in times of emergency. ...
In voting systems, Arrowâ€™s impossibility theorem, or Arrowâ€™s paradox, demonstrates that no voting system can possibly meet a certain set of reasonable criteria when there are three or more options to choose from. ...
In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ...
Social choice theory studies how individual preferences are aggregated to form a collective choice, such as, for example in voting systems. ...
| **Topics in game theory** | **Definitions** Game theory is a hybrid branch of applied mathematics and economics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ...
| Normal form game · Extensive form game · Cooperative game · Information set · Preference In game theory, normal form is a way of describing a game. ...
It has been suggested that Game tree be merged into this article or section. ...
A cooperative game is a game where groups of players (coalitions) may enforce cooperative behaviour, hence the game is a competition between coalitions of players, rather than between individual players. ...
In game theory, an information set is a set that, for a particular player, establishes all the possible moves that could have taken place in the game so far, given what that player has observed so far. ...
Preference (or taste) is a concept, used in the social sciences, particularly economics. ...
| **Equilibrium concepts** In economics, economic equilibrium often refers to an equilibrium in a market that clears: this is the case where a market for a product has attained the price where the amount supplied of a certain product equals the quantity demanded. ...
In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified. ...
| Nash equilibrium · Subgame perfection · Bayes-Nash · Trembling hand · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a kind of solution concept of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy unilaterally. ...
Subgame perfect equilibrium is an economics term used in game theory to describe an equilibrium such that players strategies constitute a Nash equilibrium in every subgame of the original game. ...
In game theory, a Bayesian game is one in which information about characteristics of the other players (i. ...
The trembling hand perfection is a notion that eliminates actions of players that are unsafe because they were chosen through a slip of the hand. ...
In game theory, a correlated equilibrium is a solution concept that is more general than the well known Nash equilibrium. ...
Sequential equilibrium is a refinement of Nash Equilibrium for extensive form games due to David M. Kreps and Robert Wilson. ...
Quasi-perfect equilibrium is a refinement of Nash Equilibrium for extensive form games due to Eric van Damme. ...
In game theory, an evolutionarily stable strategy (or ESS; also evolutionary stable strategy) is a strategy which if adopted by a population cannot be invaded by any competing alternative strategy. ...
| **Strategies** In game theory, a players strategy, in a game or a business situation, is a complete plan of action for whatever situation might arise; this fully determines the players behaviour. ...
| Dominant strategies · Mixed strategy · Grim trigger · Tit for Tat In game theory, dominance (also called strategic dominance) occurs when one strategy is better than another strategy for one player, no matter how that players opponents may play. ...
A mixed strategy is used in game theory economics to describe a strategy comprising possible moves and a probability distribution which corresponds to how frequently each move is chosen. ...
Grim Trigger is a trigger strategy in game theory for a repeated game, such as an iterated prisoners dilemma. ...
Tit for Tat is a highly-effective strategy in game theory for the iterated prisoners dilemma. ...
| **Classes of games** | Symmetric game · Perfect information · Dynamic game · Repeated game · Signaling game · Cheap talk · Zero-sum game · **Mechanism design** In game theory, a symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them. ...
Perfect information is a term used in economics and game theory to describe a state of complete knowledge about the actions of other players that is instantaneously updated as new information arises. ...
In game theory, a sequential game is a game where one player chooses his action before the others chooses theirs. ...
In game theory, a repeated game (or iterated game) is an extensive form game which consists in some number of repetitions of some base game (called a stage game). ...
Signaling games are dynamic games with two players, the sender (S) and the receiver (R). ...
Cheap Talk is a term used in Game Theory for pre-play communication which carries no cost. ...
Zero-sum describes a situation in which a participants gain (or loss) is exactly balanced by the losses (or gains) of the other participant(s). ...
| **Games** Game theory studies strategic interaction between individuals in situations called games. ...
| Prisoner's dilemma · Chicken · Stag hunt · Ultimatum game · Coordination game · Matching pennies · Minority game · Rock, Paper, Scissors · Pirate game · Dictator game Will the two prisoners cooperate to minimize total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? In game theory, the prisoners dilemma is a type of non-zero-sum game in which two players can cooperate with...
The game of chicken (also referred to as playing chicken) is a game in which two players engage in an activity that will result in serious harm unless one of them backs down. ...
In game theory, the Stag Hunt is a game first discussed by Jean-Jacques Rousseau. ...
The Ultimatum game is an experimental economics game in which two parties interact anonymously and only once, so reciprocation is not an issue. ...
In game theory, the Nash equilibrium (named after John Nash) is a kind of optimal strategy for games involving two or more players, whereby the players reach an outcome to mutual advantage. ...
Matching Pennies is the name for a simple example game used in game theory. ...
Minority Game is a game proposed by Yi-Cheng Zhang and Damien Challet from the University of Fribourg. ...
Rock, Paper, Scissors chart Listen to this article Â· (info) This audio file was created from an article revision dated 2006-07-13, and does not reflect subsequent edits to the article. ...
The Pirate Game is a simple mathematical game. ...
The dictator game is a very simple game in experimental economics, similar to the ultimatum game. ...
| **Theorems** | Minimax theorem · Purification theorems · Folk theorem · Revelation principle Minimax is a method in decision theory for minimizing the expected maximum loss. ...
In game theory, the purification theorem was contributed by Nobel laurate John Harsanyi in 1973[1]. The theorem aims to justify a puzzling aspect of mixed strategy Nash equilibria: that each player is wholly indifferent amongst each of the actions he puts non-zero weight on, yet he mixes them...
In game theory, folk theorems are a class of theorems which imply that in repeated games, any outcome is a feasible solution concept, if under that outcome the players minimax conditions are satisfied. ...
The revelation principle of economics can be stated as, To any equilibrium of a game of incomplete information, there corresponds an associated revelation mechanism that has an equilibrium where the players truthfully report their types. ...
| **Related topics** | Mathematics · Economics · Behavioral economics · Evolutionary game theory · Population genetics · Behavioral ecology · Adaptive dynamics · List of game theorists For other meanings of mathematics or math, see mathematics (disambiguation). ...
Face-to-face trading interactions among on the New York Stock Exchange trading floor In the social sciences, economics is the study of human choice behavior and how it effects the production, distribution, and consumption of scarce resources. ...
Nobel Prize in Economics winner Daniel Kahneman, was an important figure in the development of behavioral finance and economics and continues to write extensively in the field. ...
Evolutionary game theory (EGT) is the application of game theory in evolutionary biology. ...
Population genetics is the study of the distribution of and change in allele frequencies under the influence of the four evolutionary forces: natural selection, genetic drift, mutation, and migration. ...
Behavioral ecology is the study of the ecological and evolutionary basis for animal behavior, and the roles of behavior in enabling an animal to adapt to its environment (both intrinsic and extrinsic). ...
Adaptive Dynamics is a set of techniques for studying long-term phenotypical evolution developed during the 1990s. ...
This is a list of notable economists, mathematicians, political scientists, and computer scientists whose work has added substantially to the field of game theory. ...
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