Editing Evolutionary game theory (section)

===Models===
[[File:Game Diagram AniFin.gif|thumb|400px|Evolutionary game theory analyses Darwinian mechanisms with a [[system model]] with three main components –  ''population'', ''game'', and ''replicator dynamics''. The system process has four phases:<br />
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1) The model (as evolution itself) deals with a ''population'' (Pn).  The population will exhibit [[Evolution#Sources of variation|variation]] among competing individuals.  In the model this competition is represented by the game.<br>
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2) The game tests the strategies of the individuals under the rules of the game.  These rules produce different payoffs – in units of [[Fitness (biology)|fitness]] (the production rate of offspring).  The contesting individuals meet in pairwise contests with others, normally in a highly mixed distribution of the population.  The mix of strategies in the population affects the payoff results by altering the odds that any individual may meet up in contests with various strategies. The individuals leave the game pairwise contest with a resulting fitness determined by the contest outcome, represented in a ''payoff matrix''.<br> 
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3) Based on this resulting fitness each member of the population then undergoes replication or culling determined by the exact mathematics of the ''replicator dynamics process''.  This overall process then produces a ''new generation'' P(n+1).  Each surviving individual now has a new fitness level determined by the game result.<br>
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4) The new generation then takes the place of the previous one and the cycle repeats. The population mix may converge to an ''evolutionarily stable state'' that cannot be invaded by any mutant strategy.]]

Evolutionary game theory encompasses Darwinian evolution, including competition (the game), natural selection (replicator dynamics), and heredity. Evolutionary game theory has contributed to the understanding of [[group selection]], [[sexual selection]], [[altruism]], [[parental care]], [[co-evolution]], and [[ecology|ecological]] dynamics. Many counter-intuitive situations in these areas have been put on a firm mathematical footing by the use of these models.<ref name=Hammerstein>{{cite book |author1=Hammerstein, Peter |author2-link=Reinhard Selten |author2=Selten, Reinhard |chapter=Game theory and evolutionary biology |title=Handbook of Game Theory with Economic Applications |volume=2 |editor1=Aumann, R.|editor2=Hart, S. |publisher=Elsevier |date=1994 |pages=929–993 |doi=10.1016/S1574-0005(05)80060-8 |isbn=978-0-444-89427-4}}</ref>

The common way to study the evolutionary dynamics in games is through [[replicator equation]]s. These show the growth rate of the proportion of organisms using a certain strategy and  that rate is equal to the difference between the average payoff of that strategy and the average payoff of the population as a whole.<ref name=Samuelson>{{cite journal | last1=Samuelson | first1=L. | year=2002 | title=Evolution and game theory | journal=  Journal of Economic Perspectives| volume=16 | issue=2| pages=46–66 | doi=10.1257/0895330027256 | doi-access=free }}</ref> Continuous replicator equations assume infinite populations, [[continuous time]], [[complete mixing]] and that strategies breed true. Some [[attractor]]s (all global asymptotically stable fixed points) of the equations are [[evolutionarily stable state]]s.<ref name="Zeeman">{{Citation
| last1 = Zeeman | first1 = E. C.
| contribution = Population dynamics from game theory
| title = Global theory of dynamical systems
| publisher = Springer Verlag
| place = Berlin
| pages = 471–497
| date = 1980
|contribution-url = http://www.lms.ac.uk/sites/lms.ac.uk/files/1980%20Population%20dynamics%20from%20game%20theory%20(preprint).pdf}}</ref>  A strategy which can survive all "mutant" strategies is considered evolutionarily stable. In the context of animal behavior, this usually means such strategies are programmed and heavily influenced by [[genetics]], thus making any player or organism's strategy determined by these biological factors.<ref>{{cite book |author=Weibull, J. W. |date=1995 |title=Evolutionary game theory |publisher=MIT Press }}</ref><ref>{{cite book |author1=Hofbauer, J. |author2-link=Karl Sigmund |author2=Sigmund, K.  |date=1998 |title=Evolutionary games and population dynamics |publisher=Cambridge University Press }}</ref>

Evolutionary games are mathematical objects with different rules, payoffs, and mathematical behaviours. Each "game" represents different problems that organisms have to deal with, and the strategies they might adopt to survive and reproduce. Evolutionary games are often given colourful names and cover stories which describe the general situation of a particular game. Representative games include [[Chicken (game)|hawk-dove]],<ref name=Price/> [[war of attrition (game)|war of attrition]],<ref name=SelfishGene/> [[stag hunt]], [[Cheating (biology)|producer-scrounger]], [[tragedy of the commons]], and [[prisoner's dilemma]]. Strategies for these games include hawk, dove, bourgeois, prober, defector, assessor, and retaliator. The various strategies compete under the particular game's rules, and the mathematics are used to determine the results and behaviours.