Editing Evolutionary game theory (section)

===Routes to altruism===

Altruism takes place when one individual, at a cost (C) to itself, exercises a strategy that provides a benefit (B) to another individual. The cost may consist of a loss of capability or resource which helps in the battle for survival and reproduction, or an added risk to its own survival. Altruism strategies can arise through:

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! Type !! Applies to: !! Situation !! Mathematical effect
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| '''Kin selection''' – (inclusive fitness of related contestants) || Kin – genetically related individuals || Evolutionary game participants are genes of strategy. The best payoff for an individual is not necessarily the best payoff for the gene.  In any generation the player gene is ''not'' only in one individual, it is in a kin-group.  The highest fitness payoff for the kin group is selected by natural selection.  Therefore, strategies that include self-sacrifice on the part of individuals are often game winners – the evolutionarily stable strategy. Animals must live in kin-groups during part of the game for the opportunity for this altruistic sacrifice ever to take place.  || Games must take into account inclusive fitness.  Fitness function is the combined fitness of a group of related contestants – each weighted by the degree of relatedness – relative to the total genetic population.  The mathematical analysis of this gene-centric view of the game leads to Hamilton's rule, that the relatedness of the altruistic donor must exceed the cost-benefit ratio of the altruistic act itself:<ref name="Nowak & Sigmund">{{cite journal | last1=Nowak | first1=Martin A. | last2=Sigmund | first2=Karl | year=2005 | title=Evolution of indirect reciprocity | journal=Nature | volume=437 | issue=7063| pages=1293–1295 | doi=10.1038/nature04131 | pmid=16251955 |bibcode=2005Natur.437.1291N | s2cid=3153895 | url=http://pure.iiasa.ac.at/7763/1/IR-05-079.pdf }}</ref>

:''R>c/b''  R is relatedness, c the cost, b the benefit
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| '''Direct reciprocity''' || Contestants that trade favours in paired relationships || A game theoretic embodiment of "I'll scratch your back if you scratch mine".  A pair of individuals exchange favours in a multi-round game. The individuals are recognisable to one another as partnered.  The term "direct" applies because the return favour is specifically given back to the pair partner only. || The characteristics of the multi-round game produce a danger of defection and the potentially lesser payoffs of cooperation in each round, but any such defection can lead to punishment in a following round – establishing the game as a repeated prisoner's dilemma.  Therefore, the family of tit-for-tat strategies come to the fore.<ref>{{cite book |author=Axelrod, R. |date=1984 |title=The Evolution of Cooperation |pages=Chapters 1 to 4 |publisher=Penguin |isbn=978-0-14-012495-8}}</ref>

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| '''Indirect reciprocity''' || Related or non related contestants trade favours but without partnering.  A return favour is "implied" but with no specific identified source who is to give it. ||  The return favour is not derived from any particular established partner. The potential for indirect reciprocity exists for a specific organism if it lives in a cluster of individuals who can interact over an extended period of time.
It has been argued that human behaviours in establishing moral systems as well as the expending of significant energies in human society for tracking individual reputations is a direct effect of societies' reliance on strategies of indirect reciprocation.<ref>{{cite book |author=Alexander R. |title=The Biology of Moral Systems |date=1987 |publisher=Aldine Transaction |isbn=978-0-202-01174-5 |url-access=registration |url=https://archive.org/details/biologyofmoralsy0000alex }}</ref>
  
 || The game is highly susceptible to defection, as direct retaliation is impossible.  Therefore, indirect reciprocity will not work without keeping a social score, a measure of past co-operative behaviour. The mathematics lead to a modified version of Hamilton's rule where:
:''q>c/b'' where q (the probability of knowing the social score) must be greater than the cost benefit ratio<ref>{{cite journal | last1=Nowak | first1=Martin A. | s2cid=4395576 | year=1998 | title=Evolution of indirect reciprocity by image scoring | journal=Nature | volume=393 | issue=6685| pages=573–575 | doi=10.1038/31225 | pmid=9634232|bibcode=1998Natur.393..573N }}</ref><ref>{{cite journal | last1=Nowak | first1=Martin A. | last2=Sigmund | first2=Karl | year=1998 | title=The Dynamics of Indirect Reciprocity | journal=Journal of Theoretical Biology | volume=194 | issue=4| pages=561–574 | doi=10.1006/jtbi.1998.0775| pmid=9790830 | bibcode=1998JThBi.194..561N | citeseerx=10.1.1.134.2590 }}</ref>

Organisms that use social score are termed Discriminators, and require a higher level of cognition than strategies of simple direct reciprocity. As evolutionary biologist David Haig put it – "For direct reciprocity you need a face; for indirect reciprocity you need a name".
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