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In game theory, a player's strategy, in a game or a business situation, is a complete plan of action for whatever situation might arise; this fully determines the player's behaviour. A player's strategy will determine the action the player will take at any stage of the game, for every possible history of play up to that stage. Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ...
Game theory is the branch of mathematics in which games are studied: that is, models describing human behaviour. ...
Economics (deriving from the Greek words οίκω [okos], house, and νÎμω [nemo], rules hence household management) is the social science that studies the allocation of scarce resources to satisfy unlimited wants. ...
A strategy profile is a set of strategies for each player which fully specifies all actions in a game. A strategy profile must include one and only one strategy for every player.
The strategy concept is sometimes (wrongly) confused with that of a move. A move is an action taken by a player at some point during the play of a game (e.g., in chess, moving white's Bishop a2 to b3). A strategy on the other hand is a complete algorithm for playing the game, implicitly listing all moves and counter-moves for every possible situation throughout the game. The number of "moves" in a Tic Tac Toe game is 4 or 5, depending on whether you start or not, and considering that neither player can skip a turn; while the actual number of "strategies" is over 6 trillion. Flowcharts are often used to represent algorithms. ...
Tic-tac-toe, also called noughts and crosses and many other names, is a pen-and-paper game for two players, O and X, who take turns to mark the spaces in a 3×3 grid. ...
Types of strategies A pure strategy provides a complete definition in which way a player may play a game. In particular, it defines every possible choice a player might have to make, which option the player picks. A player's strategy space is the set of pure strategies available to that player. A pure strategy is a term used to refer to strategies in Game theory. ...
A mixed strategy is an assignment of a probability to each pure strategy. It defines a probability over the strategies, and reflects that, rather than choosing a particular pure strategy, the player will randomly select a pure strategy based on the distribution given by their mixed strategy. Of course, every pure strategy is a mixed strategy which selects that particular pure strategy with probability 1 and every other one with probability 0. 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. ...
The word probability derives from the Latin probare (to prove, or to test). ...
Examples of strategies
Tit for Tat Strategies in game theory are of essential importance, since the prisoners dilemma was shown never to lead to cooperation unless multiperiod strategies are considered. A highly effective strategy is "Tit for Tat". It was found in a programming contest, with several algorithms competing for the highest utility score. Game theory is a branch of applied mathematics that studies strategic situations where players choose different actions in an attempt to maximize their returns. ...
Will the two prisoners cooperate to minimise total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? The prisoners dilemma is a type of non-zero-sum game. ...
Tit for Tat is a highly-effective strategy in game theory for the iterated prisoners dilemma. ...
Roulette There is a variety of betting strategies and tactics in the Roulette game. The most famous strategy is the doubling strategy: Roulette is a casino and gambling game (Roulette is a French word meaning small wheel). A croupier turns a round roulette wheel which has 37 or 38 separately numbered pockets in which a ball must land. ...
- Set 1€
- If you lose: double your bet
- Repeat 2. until you have a profit
This was originally called the "Martingale strategy", and was formalized simply to show why it will not create an expected profit. However, it is a common (folk) strategy seen in many casinos (especially by beginning players, sometimes called "system players"). The typical casino prefers the "system player" to other types of player because the casino's risk is very low (they stand to lose only the minimum bet each time the player starts), but their potential reward is extremely high (the entire capital the gambler stakes). However, most "system players" tend to play only for a short time, and so the casino's edge is not compounded as often against the system player as against the usual roulette players (who vary their bet size less). A separate article treats the topic of martingales in probability theory. ...
In probability (and especially gambling), the expected value (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff (value). Thus, it represents the average amount one expects to win per bet if bets with identical odds are...
The Trump Taj Mahal in Atlantic City, New Jersey. ...
In politics, a capital (also called capital city or political capital — although the latter phrase has an alternative meaning based on an alternative meaning of capital) is the principal city or town associated with its government. ...
Gambling (or betting) is any behavior involving the risk of money or valuables on the outcome of a game, contest, or other event in which the outcome of that activity is partially or totally dependent upon chance. ...
Look up Edge in Wiktionary, the free dictionary. ...
- Main article: Gambler's fallacy.
The gamblers fallacy is a logical fallacy which encompasses any of the following misconceptions: A random event is more likely to occur because it has not happened for a period of time; A random event is less likely to occur because it has not happened for a period of...
Hedging Hegding is a strategy for financial investments, that searches for the lowest risk or optimal risk to performance ratio. Some kind of hedges are uniquely determined from simple parameters. The Black-Scholes equation demonstrates how a continuous stock buy and selling strategy can replicate an option without risk. In finance, a hedge is an investment that is taken out specifically to reduce or cancel out the risk in another investment. ...
The Black-Scholes model, often simply called Black-Scholes, is a model of the varying price over time of financial instruments, and in particular stocks. ...
In finance, an option is a contract whereby one party (the holder or buyer) has the right but not the obligation to exercise a feature of the contract (the option) on or before a future date (the exercise date or expiry). ...
External links - This article incorporates material from Strategy on PlanetMath, which is licensed under the GFDL.
PlanetMath is a free, collaborative, online mathematics encyclopedia. ...
| | Topics in game theory | | Definitions Game theory is a branch of applied mathematics 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 Nash, who proposed it) is a kind of solution concepts of a game involving two or more players, where no player has anything to gain by changing only his or her own strategy. ...
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 | 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). ...
Mechanism design is a sub-field of game theory. ...
| | 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? Many points in this article may be difficult to understand without a background in the elementary concepts of game theory. ...
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 Rock, Paper, Scissors, also known in Japan as Janken, is a hand game most often played by children. ...
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 · Bishop-Cannings theorem 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. ...
In game theory, the Bishop-Cannings theorem proves that all members of a mixed evolutionarily stable strategy have the same payoff, and that none of these can also be a pure evolutionarily stable strategy. ...
| | Related topics | Mathematics · Economics · Behavioral economics · Evolutionary biology · Evolutionary game theory · Population genetics · Behavioral ecology · List of game theorists Euclid, a famous Greek mathematician known as the father of geometry, is shown here in detail from The School of Athens by Raphael. ...
Buyers bargain for good prices while sellers put forth their best front in Chichicastenango Market, Guatemala. ...
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 biology is a subfield of population biology concerned with the origin and descent of species, as well as their change over time, i. ...
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). ...
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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