Evolution of Cooperation in the Presence of Higher-Order Interactions: from Networks to Hypergraphs

TL;DR

This paper investigates how higher-order group interactions, modeled by hypergraphs, influence the evolution of cooperation in structured populations, revealing that increased interaction order and heterogeneity promote cooperative behavior.

Contribution

It introduces a hypergraph-based framework to study higher-order interactions in evolutionary dynamics, extending beyond traditional pairwise network models.

Findings

Group interactions promote cooperation similarly to network reciprocity.

Heterogeneous structures with hubs enhance reciprocity as interaction order increases.

Insights into coexistence of cooperative and non-cooperative behaviors based on structural properties.

Abstract

Many real systems are strongly characterized by collective cooperative phenomena whose existence and properties still need a satisfactory explanation. Coherently with their collective nature, they call for new and more accurate descriptions going beyond pairwise models, such as graphs, in which all the interactions are considered as involving only two individuals at a time. Hypergraphs respond to this need, providing a mathematical representation of a system allowing from pairs to larger groups. In this work, through the use of different hypergraphs, we study how group interactions influence the evolution of cooperation in a structured population, by analyzing the evolutionary dynamics of the public goods game. Here we show that, likewise network reciprocity, group interactions also promote cooperation. More importantly, by means of an invasion analysis in which the conditions for a strategy to survive are studied, we show how, in heterogeneously-structured populations, reciprocity among players is expected to grow with the increasing of the order of the interactions. This is due to the heterogeneity of connections and, particularly, to the presence of individuals standing out as hubs in the population. Our analysis represents a first step towards the study of evolutionary dynamics through higher-order interactions, and gives insights into why cooperation in heterogeneous higher-order structures is enhanced. Lastly, it also gives clues about the co-existence of cooperative and non-cooperative behaviors related to the structural properties of the interaction patterns.