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. The concept is an equilibrium refinement to a Nash equilibrium. The difference between a Nash equilibrium and an ESS is that a Nash equilibrium may sometimes exist due to the assumption that rational foresight prevents players from playing an alternative strategy with no short term cost, but which will eventually be beaten by a third strategy. An ESS is defined to exclude such equilibria, and assumes that natural selection is the only force which selects against using strategies with lower payoffs. In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified. ...
Game theory is most often described as a branch of applied mathematics and economics that studies situations where players choose different actions in an attempt to maximize their returns. ...
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. ...
A stochastically stable equilibrium is a refinement of the evolutionarily stable strategy in evolutionary game theory, proposed by Dean Foster and Peyton Young. ...
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. ...
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 Bayesian game is one in which information is incomplete. ...
Professor John Maynard Smith[1], F.R.S. (6 January 1920 â€“ 19 April 2004) was a British evolutionary biologist and geneticist. ...
George R. Price (1922 - January 6, 1975) was a American population geneticist. ...
This article or section does not cite its references or sources. ...
Evolutionary game theory (EGT) is the application of game theory in evolutionary biology. ...
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 damage unless one of them backs down. ...
Game theory is most often described as a branch of applied mathematics and economics that studies situations where players choose different actions in an attempt to maximize their returns. ...
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. ...
In game theory and economic modelling, a solution concept is a process via which equilibria of a game are identified. ...
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. ...
Homo economicus, or Economic man, is the concept in some economic theories of man as both rational and It is a term used for an approximation or model of Homo sapiens that acts to obtain the highest possible well-being for himself given available information about opportunities and other constraints...
The GalÃ¡pagos Islands hold 13 species of finches that are closely related and differ most markedly in the shape of their beaks. ...
A payoff matrix or payoff function is a concept in game theory which shows what payoff each player will receive at the outcome of the game. ...
The term was introduced and defined by John Maynard Smith and George R. Price in a 1973 *Nature* paper^{[1]} and is central to Maynard Smith's (1982) book *Evolution and the Theory of Games*^{[2]}. The concept was derived from R.H. MacArthur^{[3]} and W.D. Hamilton's^{[4]} work on sex ratios, especially Hamilton's (1967) concept of an unbeatable strategy. The idea can be traced back to Ronald Fisher (1930)^{[5]} and Charles Darwin (1859)^{[6]}, (see Edwards, 1998). Professor John Maynard Smith[1], F.R.S. (6 January 1920 â€“ 19 April 2004) was a British evolutionary biologist and geneticist. ...
George R. Price (1922 - January 6, 1975) was a American population geneticist. ...
First title page, November 4, 1869 Nature is one of the oldest and most reputable scientific journals, first published on 4 November 1869. ...
Book cover Evolution and the Theory of Games is a 1982 book by the British evolutionary biologist John Maynard Smith on evolutionary game theory. ...
Robert Helmer MacArthur (April 7, 1930 â€“ November 1, 1972) was an American ecologist who made a major impact on many areas of community and population ecology. ...
This article is about the British biologist Bill Hamilton. ...
Sex ratio by country for total population. ...
In game theory, an unbeatable strategy is defined by W.D. Hamilton in his 1967 paper on sex ratios in Science. ...
Sir Ronald Aylmer Fisher, FRS (17 February 1890 â€“ 29 July 1962) was a British statistician, evolutionary biologist, and geneticist. ...
Charles Robert Darwin (12 February 1809 â€“ 19 April 1882) was an eminent English naturalist who achieved lasting fame by convincing the scientific community that species develop over time from a common origin. ...
## Nash equilibria and ESS
A Nash equilibrium is a strategy in a game such that if all players adopt it, no player will benefit by switching to play any alternative strategy. If a player choosing strategy *J* in a population where all other players play strategy *I* receives a payoff of E(*J*,*I*), then strategy *I* is a Nash equilibrium if, 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. ...
- E(
*I*,*I*) ≥ E(*J*,*I*) for any *J* This equilibrium definition allows for the possibility that strategy *J* is a neutral alternative to *I* (it scores equally, but not better). A Nash equilibrium is presumed to be stable even if *J* scores equally, on the assumption that players do not play *J* Maynard Smith and Price (1973)^{[1]} specify two conditions for a strategy *I* to be an ESS. Either Professor John Maynard Smith[1], F.R.S. (6 January 1920 â€“ 19 April 2004) was a British evolutionary biologist and geneticist. ...
George R. Price (1922 - January 6, 1975) was a American population geneticist. ...
- E(
*I*,*I*) > E(*J*,*I*), or - E(
*I*,*I*) = E(*J*,*I*) and E(*I*,*J*) > E(*J*,*J*) must be true for all *J* ≠ *I*, where E(*I*,*J*) is the expected payoff to strategy *I* when playing against strategy *J*. The first condition is sometimes called a 'strict Nash' equilibrium (Harsanyi, 1973)^{[7]}, the second is sometimes referred to as 'Maynard Smith's second condition'. There is also an alternative definition of ESS which, though it maintains functional equivalence, places a different emphasis on the role of the Nash equilibrium concept in the ESS concept. Following the terminology given in the first definition above, we have (adapted from Thomas, 1985)^{[8]}: - E(
*I*,*I*) ≥ E(*J*,*I*), and - E(
*I*,*J*) > E(*J*,*J*) In this formulation, the first condition specifies that the strategy be a Nash equilibrium, and the second specifies that Maynard Smith's second condition be met. Note that the two definitions are not precisely equivalent; for example, each pure strategy in the coordination game below is an ESS by the first definition but not the second. One advantage to this change is that the role of the Nash equilibrium in the ESS is more clearly highlighted. It also allows for a natural definition of other concepts like a weak ESS or an evolutionarily stable set (Thomas, 1985)^{[8]}.
### An example Consider the following payoff matrix, describing a coordination game: It has been suggested that this article or section be merged with normal form game. ...
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. ...
| A | B | A | 1,1 | 0,0 | B | 0,0 | 1,1 | *Coordination game* | Both strategies A and B are ESS, since a B player cannot invade a population of A players nor can an A player invade a population of B players. Here the two pure strategy Nash equilibria correspond to the two ESS. In this second game, which also has two pure strategy Nash equilibria, only one corresponds to an ESS: | C | D | C | 1,1 | 0,0 | D | 0,0 | 0,0 | *Simple game* | Here (D, D) is a Nash equilibrium (since neither player will do better by unilaterally deviating), but it is not an ESS. Consider a C player introduced into a population of D players. The C player does equally well against the population (she scores 0), however the C player does better against herself (she scores 1) than the population does against the C player. Thus, the C player can invade the population of D players. Even if a game has pure strategy Nash equilibria, it might be the case that none of the strategies are ESS. Consider the following example (known as Chicken): 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. ...
| E | F | E | 0,0 | -1,+1 | F | +1,-1 | -20,-20 | *Chicken* | There are two pure strategy Nash equilibria in this game (E, F) and (F, E). However, in the absence of an uncorrelated asymmetry, neither F nor E are ESSes. A third Nash equilibrium exists, a mixed strategy, which is an ESS for this game (see Hawk-dove game and Best response for explanation). In game theory an uncorrelated asymmetry is an informational asymmetry in a game which is otherwise symmetrical. ...
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 damage unless one of them backs down. ...
In game theory, the best response, is the strategy (or strategies) which produces the most favorable immediate outcome for the current player, taking other players strategies as given. ...
### Bishop-Cannings theorem Just as Nash equilibria can be either a pure strategy, or probabilistic mixtures of pure strategies (a mixed strategy), evolutionarily stable strategies can be either pure or mixed. A pure strategy is a term used to refer to strategies in Game theory. ...
In game theory a mixed strategy is a strategy which chooses randomly between possible moves. ...
The **Bishop-Cannings theorem** (Bishop & Cannings, 1978)^{[9]} 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^{[10]}. The same logic also applies to Nash equilibria and so the same will hold true for members of a mixed Nash as for members of a mixed ESS. 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. ...
## ESS vs. Evolutionarily Stable State - An
**ESS** or **evolutionarily stable strategy** is a strategy such that, if all the members of a population adopt it, no mutant strategy can invade. --Maynard Smith (1982)^{[2]}. - A population is said to be in an
**evolutionarily stable state** if its genetic composition is restored by selection after a disturbance, provided the disturbance is not too large. Such a population can be genetically monomorphic or polymorphic. --Maynard Smith (1982)^{[2]}. An ESS is a strategy with the property that, once virtually all members of the population use it, then no 'rational' alternative exists. An evolutionarily stable state is a dynamical property of a population to return to using a strategy, or mix of strategies, if it is perturbed from that strategy, or mix of strategies. The former concept fits within classical game theory, whereas the latter is a population genetics, dynamical system, or evolutionary game theory concept. Professor John Maynard Smith[1], F.R.S. (6 January 1920 â€“ 19 April 2004) was a British evolutionary biologist and geneticist. ...
In the context of abstract algebra or universal algebra, a monomorphism is simply an injective homomorphism. ...
In general, polymorphism describes multiple possible states for a single property (it is said to be polymorphic). ...
Professor John Maynard Smith[1], F.R.S. (6 January 1920 â€“ 19 April 2004) was a British evolutionary biologist and geneticist. ...
A population is said to be in an evolutionarily stable state if its genetic composition is restored by selection after a disturbance, provided the disturbance is not too large. ...
Game theory is most often described as a branch of applied mathematics and economics that studies situations where players choose different actions in an attempt to maximize their returns. ...
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. ...
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. ...
Evolutionary game theory (EGT) is the application of game theory in evolutionary biology. ...
Thomas (1984)^{[11]} applies the term ESS to an individual strategy which may be mixed, and evolutionarily stable population state to a population mixture of pure strategies which may be formally equivalent to the mixed ESS.
## Prisoner's dilemma and ESS Consider a large population of people who, in the iterated prisoner's dilemma, always play Tit for Tat in transactions with each other. (Since almost any transaction requires trust, most transactions can be modelled with the *prisoner's dilemma*.) If the entire population plays the *Tit-for-Tat* strategy, and a group of newcomers enter the population who prefer the *Always Defect* strategy (i.e. they try to cheat everyone they meet), the *Tit-for-Tat* strategy will prove more successful, and the *defectors* will be converted or lose out. *Tit for Tat* is therefore an ESS, *with respect to these two strategies*. On the other hand, an island of *Always Defect* players will be stable against the invasion of a few *Tit-for-Tat* players, but not against a large number of them. (see Robert Axelrod's The Evolution of Cooperation^{[12]}). 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...
Tit for Tat is a highly-effective strategy in game theory for the iterated prisoners dilemma. ...
This article is about a political scientist. ...
The Evolution of Cooperation is a book by political science professor Robert Axelrod which explores the conditions under which fundamentally selfish agents will spontaneously cooperate. ...
## ESS and human behavior The recent, controversial sciences of sociobiology and now evolutionary psychology attempt to explain animal and human behavior and social structures, largely in terms of evolutionarily stable strategies. Sociopathy (chronic antisocial/criminal behavior) has been suggested^{[13]} to be best explained as a combination of two such strategies. Sociobiology is a synthesis of scientific disciplines that explains behaviour in all species by considering the evolutionary advantages of social behaviours. ...
Evolutionary psychology (abbreviated ev-psych or EP) is a theoretical approach to psychology that attempts to explain certain mental and psychological traitsâ€”such as memory, perception, or languageâ€”as evolved adaptations, i. ...
Antisocial personality disorder (APD) is a personality disorder which is often characterised by antisocial and impulsive behaviour. ...
Although ESS were originally considered as stable states for biological evolution, it need not be limited to such contexts. In fact, ESS are stable states for a large class of adaptive dynamics. As a result ESS are used to explain human behavior without presuming that the behavior is necessarily determined by genes. Adaptive Dynamics is a set of techniques for studying long-term phenotypical evolution developed during the 1990s. ...
For other meanings of this term, see gene (disambiguation). ...
## See also - Hawk-Dove game
- War of attrition (game)
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 damage unless one of them backs down. ...
In game theory the War of attrition is a model of aggression in which two contestants compete for a resource of value V by persisting while accumulating costs at a constant rate c. ...
## References - ^
^{a} ^{b} John Maynard Smith and George R. Price (1973), The logic of animal conflict. *Nature* **246**: 15-18. - ^
^{a} ^{b} ^{c} John Maynard Smith. (1982) *Evolution and the Theory of Games*. ISBN 0-521-28884-3 **^** MacArthur, R. H. (1965). in: *Theoretical and mathematical biology* T. Waterman & H. Horowitz, eds. Blaisdell: New York. **^** W.D. Hamilton (1967) Extraordinary sex ratios. *Science* **156**, 477-488. **^** Ronald Fisher *The Genetical Theory of Natural Selection*. Clarendon Press, Oxford. **^** Charles Darwin (1859). *On the Origin of Species* **^** Harsanyi, J (1973) Oddness of the number of equilibrium points: a new proof. *Int. J. Game Theory* **2**: 235-250. - ^
^{a} ^{b} Thomas, B. (1985) On evolutionarily stable sets. *J. Math. Biology* **22**: 105-115. **^** Bishop, D.T. and C. Cannings. 1978. A generalized war of attrition. *Journal of Theoretical Biology* 70:85-124. **^** Prestwich, K. The Bishop-Cannings Theorem (an annotated version of Maynard Smith's exposition of the The Bishop-Cannings Theorem) at the College of the Holy Cross Game Theory website **^** Thomas, B. (1984) Evolutionary stability: states and strategies. *Theor. Pop. Biol.* **26** 49-67. **^** Robert Axelrod (1984) *The Evolution of Cooperation* ISBN 0-465-02121-2 **^** Mealey, L. (1995). The sociobiology of sociopathy: An integrated evolutionary model. *Behavioral and Brain Sciences* **18**: 523-599. [1] Professor John Maynard Smith[1], F.R.S. (6 January 1920 â€“ 19 April 2004) was a British evolutionary biologist and geneticist. ...
George R. Price (1922 - January 6, 1975) was a American population geneticist. ...
First title page, November 4, 1869 Nature is one of the oldest and most reputable scientific journals, first published on 4 November 1869. ...
Professor John Maynard Smith[1], F.R.S. (6 January 1920 â€“ 19 April 2004) was a British evolutionary biologist and geneticist. ...
Book cover Evolution and the Theory of Games is a 1982 book by the British evolutionary biologist John Maynard Smith on evolutionary game theory. ...
Robert Helmer MacArthur (April 7, 1930 â€“ November 1, 1972) was an American ecologist who made a major impact on many areas of community and population ecology. ...
This article is about the British biologist Bill Hamilton. ...
Science is the journal of the American Association for the Advancement of Science (AAAS). ...
Sir Ronald Aylmer Fisher, FRS (17 February 1890 â€“ 29 July 1962) was a British statistician, evolutionary biologist, and geneticist. ...
The Genetical Theory of Natural Selection is a book by Ronald Fisher. ...
Charles Robert Darwin (12 February 1809 â€“ 19 April 1882) was an eminent English naturalist who achieved lasting fame by convincing the scientific community that species develop over time from a common origin. ...
The 1859 edition of On the Origin of Species First published in 1859, The Origin of Species (full title On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life) by British naturalist Charles Darwin is one of the pivotal...
John Charles Harsanyi (Hungarian: HarsÃ¡nyi JÃ¡nos) (May 29, 1920 â€“ August 9, 2000) was a Hungarian-Australian-American business and economics professor who contributed to the study of game theory in mathematics by developing the quite revolutionary analysis of games of incomplete information, so-called Bayesian games. ...
Professor John Maynard Smith[1], F.R.S. (6 January 1920 â€“ 19 April 2004) was a British evolutionary biologist and geneticist. ...
This article is about a political scientist. ...
The Evolution of Cooperation is a book by political science professor Robert Axelrod which explores the conditions under which fundamentally selfish agents will spontaneously cooperate. ...
## Further reading - Parker, G.A. (1984) Evolutionary stable strategies. In
*Behavioural Ecology: an Evolutionary Approach* (2nd ed) Krebs, J.R. & Davies N.B., eds. pp 30-61. Blackwell, Oxford. - Hines, WGS (1987) Evolutionary stable strategies: a review of basic theory.
*Theoretical Population Biology* **31**: 195-272. - John Maynard Smith. (1982)
*Evolution and the Theory of Games*. ISBN 0-521-28884-3 Professor Geoffrey Alan Parker FRS (born 24 May 1944) is a professor of biology at the University of Liverpool. ...
Sir John Richard Krebs (born 1945) is a British biologist and a Fellow of the Royal Society. ...
Professor John Maynard Smith[1], F.R.S. (6 January 1920 â€“ 19 April 2004) was a British evolutionary biologist and geneticist. ...
Book cover Evolution and the Theory of Games is a 1982 book by the British evolutionary biologist John Maynard Smith on evolutionary game theory. ...
## External links - Evolutionarily Stable Strategies at Animal Behavior: An Online Textbook by Michael D. Breed.
- Game Theory and Evolutionarily Stable Strategies, Kenneth N. Prestwich's site at College of the Holy Cross.
view | **Topics in game theory** | **Definitions** Game theory is most often described as a branch of applied mathematics and economics that studies 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** Price of market balance In economics, economic equilibrium is simply a state of the world where economic forces are balanced and in the abscence of external shocks the (equilibrium) values of economic variables will not change. ...
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 · **ESS** · Risk dominance 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. ...
Risk dominance and payoff dominance are two related refinements of the Nash equilibrium (NE) solution concept in game theory, defined by John Harsanyi and Reinhard Selten. ...
| **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 · Tit for tat · Grim trigger In game theory, dominance occurs when one strategy is better or worse than another regardless of the strategies of a players opponents. ...
In game theory a mixed strategy is a strategy which chooses randomly between possible moves. ...
Tit for Tat is a highly-effective strategy in game theory for the iterated prisoners dilemma. ...
Grim Trigger is a trigger strategy in game theory for a repeated game, such as an 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 · Coordination game · Chicken · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock, Paper, Scissors · Pirate game · Dictator game · Public goods 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...
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. ...
It has been suggested that Peace war game be merged into this article or section. ...
The Battle of the Sexes is a two player game used in game theory. ...
In game theory, the Stag Hunt is a game first discussed by Jean-Jacques Rousseau. ...
Matching Pennies is the name for a simple example game used in game theory. ...
The Ultimatum game is an experimental economics game in which two parties interact anonymously and only once, so reciprocation is not an issue. ...
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 may 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. ...
The Public goods game is a standard of experimental economics; in the basic game subjects secretly choose how many of their private tokens to put into the public pot. ...
| **Theorems** | Minimax theorem · Purification theorems · Folk theorem · Revelation principle · Arrow's 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. ...
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. ...
In voting systems, Arrow’s impossibility theorem, or Arrow’s paradox demonstrates the impossibility of designing a set of rules for social decision making that would meet all of a certain set of criteria. ...
| **Related topics** | Mathematics · Economics · Behavioral economics · Evolutionary game theory · Population genetics · Behavioral ecology · Adaptive dynamics · List of game theorists Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ...
This article or section does not cite its references or sources. ...
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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