# A game model for the multimodality phenomena of coauthorship networks

## TL;DR

This paper introduces a game-theoretic geometric hypergraph model to simulate coauthorship network evolution, capturing cooperative mechanisms and reproducing key network properties such as degree distribution and clustering.

## Contribution

It presents a novel geometric hypergraph model incorporating kin selection and reciprocity, explaining coauthorship network phenomena with empirical validation.

## Key findings

- Model fits empirical degree distributions and clustering.
- Reveals node heterogeneity and fading effects influence network structure.
- Explains degree distribution as generalized Poisson, power law, and exponential cutoff.

## Abstract

We provided a game model to simulate the evolution of coauthorship networks, a geometric hypergraph built on a circle. The model expresses kin selection and network reciprocity, two typically cooperative mechanisms, through a cooperation condition called positive benefit-minus-cost. The costs are modelled through space distances. The benefits are modelled through geometric zones that depend on node hyperdegree, which gives an expression of the cumulative advantage on the reputations of authors. Our findings indicate that the model gives a reasonable fitting to empirical coauthorship networks on their degree distribution, node clustering, and so on. It reveals two properties of node attractions, namely node heterogeneity and fading with the growth of hyperdegrees, can deduce the dichotomy of nodes' clustering behavior and assortativity, as well as the trichotomy of degree and hyperdegree distributions: generalized Poisson, power law and exponential cutoff.