Emergence of cooperation promoted by higher-order strategy updates

TL;DR

This paper explores how higher-order strategy updates in multi-group populations influence the emergence of cooperation, revealing conditions and mechanisms that promote cooperative behavior in complex social networks.

Contribution

It introduces mathematical conditions for cooperation emergence driven by higher-order strategy updates and identifies mechanisms that significantly enhance cooperation in multi-group settings.

Findings

Higher-order strategy updates can promote cooperation under specific conditions.

Overlaps between groups significantly enhance cooperative outcomes.

A mechanism combining optimality and randomness effectively fosters cooperation.

Abstract

Cooperation is fundamental to human societies, and the interaction structure among individuals profoundly shapes its emergence and evolution. In real-world scenarios, cooperation prevails in multi-group (higher-order) populations, beyond just dyadic behaviors. Despite recent studies on group dilemmas in higher-order networks, the exploration of cooperation driven by higher-order strategy updates remains limited due to the intricacy and indivisibility of group-wise interactions. Here we investigate four categories of higher-order mechanisms for strategy updates in public goods games and establish their mathematical conditions for the emergence of cooperation. Such conditions uncover the impact of both higher-order strategy updates and network properties on evolutionary outcomes, notably highlighting the enhancement of cooperation by overlaps between groups. Interestingly, we discover that the strategical mechanism alternating optimality and randomness -- selecting an outstanding group and then imitating a random individual within this group -- can prominently promote cooperation. Our analyses further unveil that, compared to pairwise interactions, higher-order strategy updates generally improve cooperation in most higher-order networks. These findings underscore the pivotal role of higher-order strategy updates in fostering collective cooperation in complex social systems.