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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. ...

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 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. ... Reinhard Selten (born October 5, 1930) is a German economist. ... Israel Robert John Aumann (×™×©×¨××œ ××•×ž×Ÿ) (born June 8, 1930) is an Israeli mathematician and a member of the United States National Academy of Sciences. ... Karl Sigmund (b. ...

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.
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