Editing Evolutionary game theory (section)

==History==
===Classical game theory===
{{Main|Game theory}}

Classical [[non-cooperative game theory]] was conceived by [[John von Neumann]] to determine optimal strategies in competitions between adversaries. A contest involves players, all of whom have a choice of moves. Games can be a single round or repetitive. The approach a player takes in making their moves constitutes their strategy. Rules govern the outcome for the moves taken by the players, and outcomes produce payoffs for the players; rules and resulting payoffs can be expressed as [[decision tree]]s or in a [[Matrix (mathematics)|payoff matrix]]. Classical theory requires the players to make rational choices. Each player must consider the strategic analysis that their opponents are making to make their own choice of moves.<ref>{{citation |first=J. v. |last=Neumann |s2cid=122961988 |year=1928 |title=Zur Theorie der Gesellschaftsspiele |journal=[[Mathematische Annalen]] |volume=100 |issue=1 |pages=295–320 |doi=10.1007/BF01448847}} English translation: {{citation |chapter=On the Theory of Games of Strategy |editor1-first=A. W. |editor1-last=Tucker |editor2-first=R. D. |editor2-last=Luce |year=1959 |title=Contributions to the Theory of Games |volume=4 |pages=13–42 |publisher=Princeton University Press |isbn=0691079374 |chapter-url=https://books.google.com/books?id=9lSVFzsTGWsC&pg=PA13}}</ref><ref>{{cite book |first=Philip |last=Mirowski |chapter=What Were von Neumann and Morgenstern Trying to Accomplish? |editor-first=E. Roy |editor-last=Weintraub |title=Toward a History of Game Theory |location=Durham |publisher=Duke University Press |year=1992 |isbn=978-0-8223-1253-6 |pages=113–147 |chapter-url=https://books.google.com/books?id=9CHY2Gozh1MC&pg=PA113 }}</ref>

===The problem of ritualized behaviour===
[[File:John Maynard Smith.jpg|thumb|The mathematical biologist [[John Maynard Smith]] modelled evolutionary games.]]

Evolutionary game theory started with the problem of how to explain ritualized animal behaviour in a conflict situation; "why are animals so 'gentlemanly or ladylike' in contests for resources?" The leading [[ethologists]] [[Niko Tinbergen]] and [[Konrad Lorenz]] proposed that such behaviour exists [[group selection|for the benefit of the species]]. [[John Maynard Smith]] considered that incompatible with Darwinian thought,<ref>{{cite book |author=Cohen, Marek |title=A Reason for Everything |date=2004 |publisher=Faber and Faber |pages=231–240 |isbn=978-0-571-22393-0}}</ref> where selection occurs at an individual level, so self-interest is rewarded while seeking the common good is not. Maynard Smith, a mathematical biologist, turned to game theory as suggested by George Price, though [[Richard Lewontin]]'s attempts to use the theory had failed.<ref>Video Interview – John Maynard Smith – [http://www.webofstories.com/play/7294?o=MS The creation of Evolutionary Game Theory]</ref>

===Adapting game theory to evolutionary games===

Maynard Smith realised that an evolutionary version of game theory does not require players to act rationally—only that they have a strategy. The results of a game show how good that strategy was, just as [[evolution]] tests alternative strategies for the ability to survive and reproduce. In biology, strategies are genetically inherited traits that control an individual's action, analogous with computer programs.  The success of a strategy is determined by how good the strategy is in the presence of competing strategies (including itself), and of the frequency with which those strategies are used.<ref>{{cite book |author=Vincent, Thomas |title=Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics |url=https://archive.org/details/evolutionarygame00tlvi |url-access=limited |date=2005 |publisher=Cambridge University Press |pages=[https://archive.org/details/evolutionarygame00tlvi/page/n90 72]–87 |isbn=978-0-521-84170-2}}</ref> Maynard Smith described his work in his book ''[[Evolution and the Theory of Games]]''.<ref name=JMSbook>{{cite book |author-link=John Maynard Smith |last=Maynard Smith |first=John |date=1982 |title=Evolution and the Theory of Games |isbn=978-0-521-28884-2|title-link=Evolution and the Theory of Games |publisher=Cambridge University Press }}</ref>

Participants aim to produce as many replicas of themselves as they can, and the payoff is in units of fitness (relative worth in being able to reproduce). It is always a multi-player game with many competitors.  Rules include replicator dynamics, in other words how the fitter players will spawn more replicas of themselves into the population and how the less fit will be [[Culling|culled]], in a [[replicator equation]]. The replicator dynamics models heredity but not mutation, and assumes asexual reproduction for the sake of simplicity. Games are run repetitively with no terminating conditions. Results include the dynamics of changes in the population, the success of strategies, and any equilibrium states reached. Unlike in classical game theory, players do not choose their strategy and cannot change it: they are born with a strategy and their offspring inherit that same strategy.<ref>{{cite book |author=Dugatkin, Lee |title=Game Theory and Animal Behavior |date=1998  |publisher=Oxford University Press |isbn=978-0-19-509692-7 |pages=2–20}}</ref>