Evolutionary game theory (EGT) is the application of population genetics-inspired models of change in gene frequency in populations to game theory. Population genetics is the study of the Allele frequency distribution and change under the influence of the four evolutionary forces Natural selection, Genetic Game theory is a branch of Applied mathematics that is used in the Social sciences (most notably Economics) Biology, Engineering, It differs from classical game theory by focusing on the dynamics of strategy change more than the properties of strategy equilibria. Game theory is a branch of Applied mathematics that is used in the Social sciences (most notably Economics) Biology, Engineering, In Mathematics, the point \tilde \mathbf{x}\in \mathbb{R}^n is an equilibrium point for the Differential equation \frac{d\mathbf{x}}{dt} Despite its name, evolutionary game theory is practised more by economists than biologists.
The common methodology to study the evolutionary dynamics in games is through replicator equations. In mathematics the replicator equation is deterministic monotone non-linear and non-innovative game dynamic used in Evolutionary game theory. Continuous replicator equations assume infinite populations, continuous time, complete mixing and that strategies breed true. A continuous signal or a continuous-time signal is a varying quantity (a signal) that is expressed as a function of a real-valued domain usually time In Evolutionary game theory, complete mixing refers to an assumption about the type of interactions that occur between individual organisms A true breeding organism, sometimes also called a pure-bred is an Organism having certain biological traits which are passed on to all subsequent generations The attractors (stable fixed points) of the equations are equivalent with evolutionarily stable states. An attractor is a set to which a Dynamical 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
- Behavioral ecology
- Dynamical systems
- Evolution and the Theory of Games (book)
- Evolutionary stable strategy
- Gene-centered view of evolution
References
- Maynard Smith, J. (1982) Evolution and the Theory of Games. Evolutionary invasion analysis, also known as adaptive dynamics, is a set of techniques for studying long-term Phenotypical Evolution developed during the 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 Dynamical systems theory is an area of Applied mathematics used to describe the behavior of complex Dynamical systems usually by employing Differential Evolution and the Theory of Games is a 1982 Book by the British evolutionary biologist John Maynard Smith on Evolutionary In Game theory and Behavioural ecology, an evolutionarily stable strategy (ESS is a strategy which if adopted by a population of players The gene-centered view of evolution, gene selection theory or selfish gene theory holds that Natural selection acts through differential survival of competing Maynard Smith redirects here -- for other uses see Maynard Smith (disambiguation Professor John Maynard Smith, F Evolution and the Theory of Games is a 1982 Book by the British evolutionary biologist John Maynard Smith on Evolutionary
- P. Hammerstein and R. Selten, "Game theory and evolutionary biology", in Handbook of Game Theory with Economic Applications, R. J. Aumann and S. Reinhard Selten ( October 5, 1930) is a German economist. Selten was born in Breslau (Wrocław in Lower Silesia Robert John Aumann ( Hebrew name: Yisrael Aumann he ישראל אומן (born June 8, 1930) is an Israeli Mathematician and a 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. Karl Sigmund (b July 26, 1945 in Gars am Kamp, Lower Austria) is a Professor of Mathematics at the University of Vienna and one of the pioneers 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
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
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