Editing Evolutionary game theory (section)

==Extending the model==

A [[mathematical model]] analysing the behaviour of a system needs initially to be as simple as possible to aid in developing a base understanding the fundamentals, or “first order effects”, pertaining to what is being studied.  With this understanding in place it is then appropriate to see if other, more subtle, parameters (second order effects) further impact the primary behaviours or shape additional behaviours in the system.   Following Maynard Smith's seminal work in evolutionary game theory, the subject has had a number of very significant extensions which have shed more light on understanding evolutionary dynamics, particularly in the area of altruistic behaviors.  Some of these key extensions to evolutionary game theory are:

[[File:SpatialExamp.gif|thumb|upright|150px|''' A Spatial Game'''<br />In a spatial evolutionary game contestants meet in contests at fixed grid positions and only interact with immediate neighbors. Shown here are the dynamics of a Hawk Dove contest, showing Hawk and Dove contestants as well as the changes of strategy taking place in the various cells]]

=== Spatial games ===

Geographic factors in evolution include [[gene flow]] and [[horizontal gene transfer]].  Spatial game models represent geometry by putting contestants in a lattice of cells: contests take place only with immediate neighbours. Winning strategies take over these immediate neighbourhoods and then interact with adjacent neighbourhoods. This model is useful in showing how pockets of co-operators can invade and introduce altruism in the Prisoners Dilemma game,<ref>{{cite book |author=Nowak, Martin |title=Evolutionary Dynamics |url=https://archive.org/details/evolutionarydyna00nowa_778 |url-access=limited |date=2006 |publisher=Harvard University Press |pages=[https://archive.org/details/evolutionarydyna00nowa_778/page/n165 152]–154 |isbn=978-0-674-02338-3}}</ref> where Tit for Tat (TFT) is a Nash Equilibrium but NOT also an ESS. Spatial structure is sometimes abstracted into a general network of interactions.<ref>{{Cite journal | url=http://egtheory.wordpress.com/2012/03/21/spatial-structure/ | title=Statistical mechanics of complex networks| journal=Reviews of Modern Physics| volume=74| issue=1| pages=47–97| year=2002| last1=Albert| first1=Reka| last2=Barabasi| first2=Albert-Laszlo| doi=10.1103/RevModPhys.74.47| citeseerx=10.1.1.242.4753| bibcode=2002RvMP...74...47A| arxiv=cond-mat/0106096| s2cid=60545}}</ref><ref>H. Tembine, E. Altman, R. El Azouzi, Y. Hayel: Evolutionary Games in Wireless Networks. IEEE Transactions on Systems, Man, and Cybernetics, Part B 40(3): 634–646 (2010)</ref> This is the foundation of [[evolutionary graph theory]].

===Effects of having information===

In evolutionary game theory as in conventional [[game theory]] the effect of Signalling (the acquisition of information) is of critical importance, as in Indirect Reciprocity in Prisoners Dilemma (where contests between the SAME paired individuals are NOT repetitive). This models the reality of most normal social interactions which are non-kin related. Unless a probability measure of reputation is available in Prisoners Dilemma only direct reciprocity can be achieved.<ref name="Nowak & Sigmund" />  With this information indirect reciprocity is also supported.

Alternatively, agents might have access to an arbitrary signal initially uncorrelated to strategy but becomes correlated due to evolutionary dynamics. This is the [[green-beard effect]] (see side-blotched lizards, above) or evolution of ethnocentrism in humans.<ref>{{Cite journal | url=http://egtheory.wordpress.com/2012/06/13/evolution-of-ethnocentrism/ | doi=10.1177/0022002706293470| title=The Evolution of Ethnocentrism| journal=Journal of Conflict Resolution| volume=50| issue=6| pages=926–936| year=2006| last1=Hammond| first1=Ross A.| last2=Axelrod| first2=Robert| s2cid=9613947}}</ref> Depending on the game, it can allow the evolution of either cooperation or irrational hostility.<ref>Kaznatcheev, A. (2010, March). [http://www.cs.mcgill.ca/~akazna/kaznatcheev20100910.pdf Robustness of ethnocentrism to changes in inter-personal interactions]. In ''Complex Adaptive Systems–AAAI Fall Symposium''.</ref>

From molecular to multicellular level, a [[signaling game]] model with information asymmetry between sender and receiver might be appropriate, such as in mate attraction<ref name="Grafen 1990 517–546"/> or evolution of translation machinery from RNA strings.<ref>{{cite journal |author1=Jee, J. |author2=Sundstrom, A. |author3=Massey, S.E. |author4=Mishra, B.  | year=2013 | title= What can information-asymmetric games tell us about the context of Crick's 'Frozen Accident'? | journal=Journal of the Royal Society Interface | volume=10 | issue=88 | page=20130614 | doi=10.1098/rsif.2013.0614 | pmid=23985735 | pmc=3785830}}</ref>

===Finite populations===

Many evolutionary games have been modelled in finite populations to see the effect this may have, for example in the success of mixed strategies.