Reciprocityn

Reciprocityn is a theoretical construct in sociology and network science that describes how reciprocal behavior can propagate through a social or informational network beyond immediate exchanges. The term uses the variable n to denote the maximum distance, in edges, over which reciprocity is assumed to influence actions of other agents.

In its general form, reciprocityn posits that an agent's propensity to return a cooperative act is influenced by neighbors up to n degrees away; actions within distance d contribute with decay function f(d), and reciprocity beyond distance n is not assumed.

The term has appeared in theoretical discussions and some simulations, but it has not achieved formal standardization; it is often treated as a thought experiment or model parameter in agent-based studies.

Applications span online communities, peer-to-peer networks, collaborative platforms, and organizational settings, where designers seek to foster cooperation by aligning incentives not only with direct partners but with broader, depth-n networks.

Critics note that measuring multi-step reciprocity requires detailed network data, assumes bounded rationality and consistent incentives, and may be vulnerable to strategic exploitation or misaligned information, limiting predictive power in heterogeneous environments.

See also reciprocity, social exchange theory, cascade effects, network theory.