Evolutionary Game Theory - Routes To Altruism

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 it may consist of an added risk to its own survival – i.e. incurring a higher probability of non-survival for itself. Altruism strategies arise in a number of ways:

Type	Applies to:	Situation	Mathematical effect
Kin Selection –(inclusive fitness of related contestants )	Kin – genetically related individuals	Evolutionary Game participants are actually “genes of strategy”. So it follows that what is the best payoff for an individual is not necessarily what is the best payoff for the gene. In any generation the player gene is NOT only in one individual, it is in a Kin-Group. What produces the highest fitness payoff for the Kin Group is the better strategy and will be selected by natural selection. Therefore strategies that include “self-sacrifice” on the part of individuals are often the “game winner” – the evolutionary stable strategy. Of course animals must necessarily live in kin-group during some life phase or over all of the game to afford the opportunity for this altruistic sacrifice to ever 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 genetic relatedness of the altruistic donor must exceed the cost-benefit ratio of the altruistic act itself, in mathematical terms: R>c/b R is relatedness, c the cost, b the benefit
Direct reciprocity	Related or non related contestants that “trade favours” in paired relationships	A game theoretic embodiment of the adage “I’ll scratch your back if you scratch mine”. A pair of individuals exchange favours in a multi-round game in which both individuals are involved. The individuals in the pair are specifically 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, however any such defection can lead to subsequent "punishment" in a following round – establishing the game as that of classical repeated Prisoners Dilemma. Therefore, the family of tit-for-tat strategies come to the fore.
Indirect Reciprocity	Related or non related contestants “trade favours” but not with partnering involved. A return favour is “implied” but with no specific identified source who is to give it.	This behaviour is akin to “I’ll scratch your back, you scratch someone elses back, another someone else will scratch mine (probably)". 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 system as well as the expending of significant energies in human society for tracking individual reputation is a direct effect of societies reliance on strategies of indirect reciprocation.	The game is highly susceptible to defection, particularly as direct retaliation becomes essentially impossible. Therefore indirect reciprocity will not work mathematically unless some additional factor is at play to verify that any individual being granted a favour is “trustworthy” to return the favour in the sharing group and insuring the punishment (non-reward) of defectors for “misbehaving”. This requires essentially keeping a "social score", a measure of the past co-operative behaviour. The mathematics leads 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 Organisms that use this sort of social score as an extended modification of the tit-for-tat variant strategies are termed Discriminators. Different discrimination algorithms exist for determining social scores, but in general all of these require a much higher level of cognition to exist than strategies of simple direct reciprocity. As David Haig, a noted evolutionary biologist succinctly put it - "For direct reciprocity you need a face; for indirect reciprocity you need a name".

Type

Applies to:

Situation

Mathematical effect

Kin Selection –(inclusive fitness of related contestants )

Kin – genetically related individuals

Evolutionary Game participants are actually “genes of strategy”. So it follows that what is the best payoff for an individual is not necessarily what is the best payoff for the gene. In any generation the player gene is NOT only in one individual, it is in a Kin-Group. What produces the highest fitness payoff for the Kin Group is the better strategy and will be selected by natural selection. Therefore strategies that include “self-sacrifice” on the part of individuals are often the “game winner” – the evolutionary stable strategy. Of course animals must necessarily live in kin-group during some life phase or over all of the game to afford the opportunity for this altruistic sacrifice to ever 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 genetic relatedness of the altruistic donor must exceed the cost-benefit ratio of the altruistic act itself, in mathematical terms:

R>c/b R is relatedness, c the cost, b the benefit

Direct reciprocity

Related or non related contestants that “trade favours” in paired relationships

A game theoretic embodiment of the adage “I’ll scratch your back if you scratch mine”. A pair of individuals exchange favours in a multi-round game in which both individuals are involved. The individuals in the pair are specifically 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, however any such defection can lead to subsequent "punishment" in a following round – establishing the game as that of classical repeated Prisoners Dilemma. Therefore, the family of tit-for-tat strategies come to the fore.

Indirect Reciprocity

Related or non related contestants “trade favours” but not with partnering involved. A return favour is “implied” but with no specific identified source who is to give it.

This behaviour is akin to “I’ll scratch your back, you scratch someone elses back, another someone else will scratch mine (probably)". 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 system as well as the expending of significant energies in human society for tracking individual reputation is a direct effect of societies reliance on strategies of indirect reciprocation.

The game is highly susceptible to defection, particularly as direct retaliation becomes essentially impossible. Therefore indirect reciprocity will not work mathematically unless some additional factor is at play to verify that any individual being granted a favour is “trustworthy” to return the favour in the sharing group and insuring the punishment (non-reward) of defectors for “misbehaving”. This requires essentially keeping a "social score", a measure of the past co-operative behaviour. The mathematics leads 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

Organisms that use this sort of social score as an extended modification of the tit-for-tat variant strategies are termed Discriminators. Different discrimination algorithms exist for determining social scores, but in general all of these require a much higher level of cognition to exist than strategies of simple direct reciprocity. As David Haig, a noted evolutionary biologist succinctly put it - "For direct reciprocity you need a face; for indirect reciprocity you need a name".

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