Cooperation

A social interaction in which a participant provides a benefit to another; classifications distinguish immediate actor benefits from evolutionary altruism. Group benefit alone does not explain persistence of an individually costly contribution.

Group selection is a contribution to natural selection arising because groups differ in their survival, growth or production of descendant groups. A heritable trait can spread through greater success of groups containing it even while its frequency declines within each mixed group. For cooperation, the essential question is whether this difference between groups can overcome an individual's cost in biological fitness.

Consider a hypothetical biological population with two groups of 100 individuals: one contains 80 cooperators and the other 20. Initially, the overall cooperative fraction is $100/200=0.50$. Suppose the first group grows to 200 individuals with 75% cooperators, while the second remains at 100 with 15% cooperators. Cooperation has declined within both groups, yet the combined cooperative fraction isThe more cooperative group now contributes more individuals to the total. These invented counts illustrate why within-group change and changes in group weights must both be measured; they do not establish the cause of a real group's growth.

In a 2006 model, Arne Traulsen and Martin A. Nowak made this mechanism explicit: individuals reproduced within groups, groups could split on reaching a size limit, and a split displaced another group. Groups with more cooperators could split more often despite the within-group advantage of withholding help. The population structure and rules governing group persistence therefore mattered alongside individual biological fitness.^[ref]

Network reciprocity is the promotion of cooperation by the pattern of interactions in a biological population. When cooperators interact preferentially with other cooperators, their help can sustain local clusters. A graph makes the mechanism precise: individuals occupy graph vertices, and graph edges specify who interacts with whom. Recognition of a previous helper is not required.

In the donation game, let each cooperator pay a cost $c$ per neighbour and supply benefit $b$ to that neighbour. On a regular graph with four neighbours per individual, a cooperator surrounded by four cooperators receives payoff $4b-4c$; an isolated cooperator surrounded by nonhelpers receives $-4c$. Thus the same behaviour has different consequences in different local arrangements.

Hisashi Ohtsuki and colleagues derived the approximate condition $b/c>k$ for natural selection to favour cooperation on large regular graphs of degree of a vertex $k$, under weak selection. Their updating rule first removed a random individual, then let its neighbours compete for the vacancy according to biological fitness. For $k=4$, $b=5$ and $c=1$ satisfy the asymptotic condition. The rule concerns fixation probability under stated assumptions; changing the order of death and reproduction can change the result.^[ref]

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.^[ref]

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

A resource or service whose effects can benefit others as well as its producer. The spatial scale of benefits, production cost and competitive setting determine exploitation incentives.

Discrimination among potential or previous partners. Repeat interactions support partner-specific responses only if the relevant information can be retained or reliably associated with a location.

Information about an individual’s past behaviour that can alter its later interactions, including interactions with different partners. Reputation-based explanations require a mechanism for acquiring and using that information.

A mechanism in which helping a persistent partner improves the actor’s later direct returns through that partner’s survival or productivity, without requiring an explicit repayment rule.

Conditional cooperation based on previous interaction with the same partner. Repeated-game support for cooperation depends on encounter continuation, observation and the competing strategies.

Selection of interaction partners in a way that can favour useful contributions through access to future benefits. Its effects depend on available alternatives, information and switching costs.

An interaction in which access to partners and exchange alternatives change the terms of cooperation. Encounter rate and partner availability can have effects different from relationship persistence.

In evolutionary analysis, an action with a direct fitness cost to its actor and a benefit to another. The comparison depends on the specified alternative and timescale.