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Encyclopedia > Evolutionary game theory

Evolutionary game theory (EGT) is the application of population genetics-inspired models of change in gene frequency in populations to game theory. It differs from classical game theory by focusing on the dynamics of strategy change more than the properties of strategy equilibria. Despite its name, evolutionary game theory is practised more by economists than biologists. 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. ... Game theory is often described as a branch of applied mathematics and economics that studies situations where multiple players make decisions in an attempt to maximize their returns. ... Game theory is often described as a branch of applied mathematics and economics that studies situations where multiple players make decisions in an attempt to maximize their returns. ... In mathematics, the point is an equilibrium point for the differential equation if for all . ...


The common methodology to study the evolutionary dynamics in games is through replicator equations. Replicator equations assume infinite populations, continuous time, complete mixing and that strategies breed true. The attractors (stable fixed points) of the equations are equivalent with evolutionarily stable states. The replicator equation is a differential equation that defines the dynamics of evolutionary games. ... Continuous time occurs when time is sampled continuously. ... In evolutionary game theory, complete mixing refers to an assumption about the type of interactions that occur between individual organisms. ... A true breeding organism is an organism having a certain trait which is passed on to all subsequent generations when bred with another true breeding organism for the same trait. ... In dynamical systems, an attractor is a set to which the system evolves after a long enough time. ... 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. ...


See also

Adaptive Dynamics is a set of techniques for studying long-term phenotypical evolution developed during the 1990s. ... 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). ... In engineering and mathematics, a dynamical system is a deterministic process in which a functions value changes over time according to a rule that is defined in terms of the functions current value. ... Book cover Evolution and the Theory of Games is a 1982 book by the British evolutionary biologist John Maynard Smith on evolutionary game theory. ... The evolutionarily stable strategy (or ESS; also evolutionary stable strategy) is a central concept in game theory introduced by John Maynard Smith and George R. Price in 1973 (a full account is given by Maynard Smith, 1982). ...

References

  • Maynard Smith, J. (1982) Evolution and the Theory of Games.
  • P. Hammerstein and R. Selten, "Game theory and evolutionary biology", in Handbook of Game Theory with Economic Applications, R. J. Aumann and S. Hart, Eds. (Elsevier, Amsterdam, 1994), vol. 2, pp. 929-993
  • Hofbauer, J. and Sigmund, K. (1998) Evolutionary games and population dynamics, Cambridge University Press
  • Taylor, P. D. (1979). Evolutionarily Stable Strategies with Two Types of Players J. Appl. Prob. 16, 76-83.
  • Taylor, P. D., and Jonker, L. B. (1978). Evolutionarily Stable Strategies and Game Dynamics Math. Biosci. 40, 145-156.
  • Weibull, J. W. (1995) Evolutionary game theory, MIT Press

Professor John Maynard Smith[1], F.R.S. (6 January 1920 – 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. ... Reinhard Selten (born October 5, 1930) is a German economist. ... Israel Robert John Aumann (ישראל אומן) (born June 8, 1930) is an Israeli mathematician and a member of the United States National Academy of Sciences. ... Karl Sigmund (b. ...

External links

  • EGT at the Stanford Encyclopedia of Philosophy
  • Evolving Artificial Moral Ecologies at The Centre for Applied Ethics, University of British Columbia
  • Evolutionary game theory at the Open Directory Project


The Open Directory Project (ODP), also known as dmoz (from , its original domain name), is a multilingual open content directory of World Wide Web links owned by Netscape that is constructed and maintained by a community of volunteer editors. ... 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. ... Hardy–Weinberg principle for two alleles: the horizontal axis shows the two allele frequencies p and q, the vertical axis shows the genotype frequencies and the three possible genotypes are represented by the different glyphs In population genetics, the Hardy–Weinberg principle (HWP) (also Hardy–Weinberg equilibrium (HWE), or Hardy... Genetic linkage occurs when particular alleles are inherited jointly. ... Linkage disequilibrium (LD) is the non-random association of alleles at two or more loci on a chromosome. ... In population genetics, Ronald Fishers fundamental theorem of natural selection was originally stated as: The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time. ... The neutral theory of molecular evolution (also, simply the neutral theory of evolution) is an influential theory that was introduced with provocative effect by Motoo Kimura in the late 1960s and early 1970s. ... For other uses, see Selection (disambiguation). ... For other uses, see Natural selection (disambiguation). ... Illustration from The Descent of Man and Selection in Relation to Sex by Charles Darwin showing the Tufted Coquette Lophornis ornatus, female on left, ornamented male on right. ... This Chihuahua mix and Great Dane show the wide range of dog breed sizes created using artificial selection. ... Ecological selection (or environmental selection or survival selection or individual selection or asexual selection) refers to natural selection minus sexual selection, i. ... The process by which an evolutionary neutral or in some cases deleterious allele or mutation may spread through the gene pool by virtue of being linked to a beneficial mutation. ... The term background selection refers to the reduction in genetic variation that occurs in the genomic area surrounding a gene that repeatedly mutates to a bad version. ... In population genetics, genetic drift is the statistical effect that results from the influence that chance has on the success of alleles (variants of a gene). ... Species with a small population size are subject to a higher chance of extinction because their small population size makes them more vulnerable to genetic drift, resulting in stochastic variation in their gene pool, their demography and their environment. ... A population bottleneck (or genetic bottleneck) is an evolutionary event in which a significant percentage of a population or species is killed or otherwise prevented from reproducing, and the population is reduced by 50% or more, often by several orders of magnitude. ... Simple illustration of founder effect. ... In genetics, coalescent theory is a retrospective model of population genetics that traces all alleles of a gene in a sample from a population to a single ancestral copy shared by all members of the population, known as the most recent common ancestor (MRCA; sometimes also termed the coancestor to... Sir Ronald Aylmer Fisher, FRS (17 February 1890 – 29 July 1962) was an English statistician, evolutionary biologist, and geneticist. ... John Burdon Sanderson Haldane (November 5, 1892 – December 1, 1964), who normally used J.B.S. as a first name, was a British geneticist and evolutionary biologist. ... Sewall Green Wright ForMemRS (December 21, 1889 – March 3, 1988) was an American geneticist known for his influential work on evolutionary theory. ... This article is about evolution in biology. ... Microevolution is the occurrence of small-scale changes in allele frequencies in a population, over a few generations, also known as change at or below the species level. ... In evolutionary biology, fitness landscapes or adaptive landscapes are used to visualize the relationship between genotypes (or phenotypes) and replicatory success. ... Genetic genealogy is the application of genetics to traditional genealogy. ... This is a list of topics in evolutionary biology and evolution. ...

 view  Topics in game theory

Definitions Game theory is often described as a branch of applied mathematics and economics that studies situations where multiple players make decisions 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 · Bayesian-Nash · Perfect Bayesian · Trembling hand · Proper equilibrium · Epsilon-equilibrium · Correlated equilibrium · Sequential equilibrium · Quasi-perfect equilibrium · Evolutionarily stable strategy · 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. ... 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. ... Proper equilibrium is a refinement of Nash Equilibrium due to Roger B. Myerson. ... In game theory, an Epsilon-equilibrium is a strategy profile that approximately satisfies the condition of Nash Equilibrium. ... 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. ... 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 · Collusion 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. ... Look up collusion in Wiktionary, the free dictionary. ...

Classes of games

Symmetric game · Perfect information · Dynamic game · Repeated game · Signaling game · Cheap talk · Zero-sum game · Mechanism design · Stochastic game · Nontransitive game 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. ... In game theory, a stochastic game is a competitive game with probabilistic transitions played by two players. ... A non-transitive game is a game for which the various strategies produce one or more loops of preferences. ...

Games Game theory studies strategic interaction between individuals in situations called games. ...

Prisoner's dilemma · Traveler's dilemma · Coordination game · Chicken · Volunteer's dilemma · Dollar auction · Battle of the sexes · Stag hunt · Matching pennies · Ultimatum game · Minority game · Rock, Paper, Scissors · Pirate game · Dictator game · Public goods game · Nash bargaining game · Blotto games  · War of attrition 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 (sometimes abbreviated PD) is a type of non-zero-sum game in which two players... In game theory, the travelers dilemma (sometimes abbreviated TD) is a type of non-zero-sum game in which two players attempt to maximise their own payoff, without any concern for the other players payoff. ... 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. ... For other uses, see Chicken (disambiguation). ... The Volunteers dilemma game models a situation in which each of N players faces the decision of either making a small sacrifice from which all will benefit or freeriding. ... On eBay, where an auction has a starting price of $1 ... 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 ( info/dl) This audio file was created from an article revision dated 2006-07-13, and may not reflect subsequent edits to the article. ... From Howard Pyles Book of Pirates 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. ... The Nash Bargaining Game is a simple two player game used to model bargaining interactions. ... Blotto games (or Colonel Blotto games) constitute a class of two-person zero-sum games in which the players are tasked to simultaneously distribute limited resources over several objects, with the gain (or payoff) being equal to the sum of the gains on the individual objects. ... 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. ...

Theorems

Minimax theorem · Purification theorems · Folk theorem · Revelation principle · Arrow's theorem “Minmax” redirects here. ... 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. ...


  Results from FactBites:
 
Game theory - Wikipedia, the free encyclopedia (3866 words)
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.
Game theorists may assume players always act rationally to maximize their wins (the Homo economicus model), but real humans often act either irrationally, or act rationally to maximize the wins of some larger group of people (altruism).
Game theory experienced a flurry of activity in the 1950s, during which time the concepts of the core, the extensive form game, fictitious play, repeated games, and the Shapley value were developed.
  More results at FactBites »

 
 

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