Indirect reciprocity (source code)

= Indirect reciprocity

<Indirect reciprocity> is <cooperation> in which helping one individual affects the help received from a different individual, often through <reputation>. For example, individual A helps B; C observes the act and later helps A. B need never repay A. In <direct reciprocity>, by contrast, the same pair exchanges help over repeated encounters.

<Martin A. Nowak> and <Karl Sigmund>'s 1998 model assigned individuals an image score reflecting earlier helping. Potential donors used that information when deciding whom to help, and successful strategies became more frequent. In the model, let $c$ be the donor's cost, $b$ the recipient's benefit, and $q$ the probability of knowing a recipient's <reputation>. An <evolutionarily stable strategy> based on helping required $q>c/b$. With $c=1$ and $b=4$, the threshold is $q>0.25$; merely observing that help is beneficial does not meet this information requirement.<Evolution of indirect reciprocity by image scoring by Martin A. Nowak and Karl Sigmund>[Nature 393, pp. 573–577; abstract and analytic stability condition]{ref}

The condition belongs to this reputation model. It is not a universal numerical threshold for every system described as <indirect reciprocity>.