Cooperation dynamics of generalized reciprocity in state-based social dilemmas

TL;DR

This paper introduces a framework for understanding how generalized reciprocity influences cooperation in networked social dilemmas, revealing that cooperation naturally emerges as the dominant stable state across various complex networks.

Contribution

It develops a unified dynamical systems approach to analyze cooperation via generalized reciprocity in diverse social dilemmas on complex networks, highlighting the role of network structure.

Findings

Cooperation always emerges as the unique attractor maximizing overall cooperation.

Network structure influences cooperation levels through a local centrality measure.

The framework applies to multiple social dilemmas, including public goods and donation games.

Abstract

We introduce a framework for studying social dilemmas in networked societies where individuals follow a simple state-based behavioral mechanism based on generalized reciprocity, which is rooted in the principle "help anyone if helped by someone". Within this general framework, which applies to a wide range of social dilemmas including, among others, public goods, donation and snowdrift games, we study the cooperation dynamics on a variety of complex network examples. By interpreting the studied model through the lenses of nonlinear dynamical systems, we show that cooperation through generalized reciprocity always emerges as the unique attractor in which the overall level of cooperation is maximized, while simultaneously exploitation of the participating individuals is prevented. The analysis elucidates the role of the network structure, here captured by a local centrality measure which uniquely quantifies the propensity of the network structure to cooperation, by dictating the degree of cooperation displayed both at microscopic and macroscopic level. We demonstrate the applicability of the analysis on a practical example by considering an interaction structure that couples a donation process with a public goods game.