Small world yields optimal public goods in presence of both altruistic and selfish cooperators

TL;DR

This paper introduces a coevolutionary game model incorporating social conformity and punishment in spatial public goods games, revealing that small-world networks optimize cooperation and altruism.

Contribution

It extends cooperation theory by integrating conformity effects and punishment in spatial networks, highlighting the unique role of small-world topology in promoting cooperation.

Findings

Small-world networks enable cooperators to outperform defectors.

Altruistic cooperators thrive in small-world and random networks.

Regular lattices favor selfish cooperators due to network reciprocity.

Abstract

Empirical studies have shown that individuals' behaviors are largely influenced by social conformity, including punishment. However, a coevolutionary theoretical framework that takes into account effects of conformity on individuals' punishment behaviors has not been put forward yet. Herein we propose a coevolutionary game model to extend the theory of cooperation with conformity in spatial public goods game by considering pool punishment, as well as two converse feedback modes of conformity that strongly affect cooperators' punishment behaviors. We focus on how different parameters and spatial structures govern evolutionary dynamics on three different kinds of networks by employing mean-field analysis based on replicator dynamics and Monte Carlo simulations. On regular lattices, defectors are overall extincted since cooperators, especially selfish cooperators, have great evolutionary advantages due to strong network reciprocity, and at the same time the number of altruistic cooperators decays. Conversely, abundant shortcuts in regular random networks lead to the prevalence of altruistic cooperators, but cooperators suffer from free-riding behaviors of defectors. Of particular interest, we find that small-world topology can simultaneously help cooperators successfully outperform defectors by means of strong network reciprocity, and enable rich contacting opportunities with defectors to facilitate the expansion of altruistic cooperators. Therefore, we clarify that small world is the optimal topology subject to the dominance of altruistic cooperators.