An Evolution Model of Complex Systems with Simultaneous Cooperation and Competition

TL;DR

This paper investigates the evolution mechanisms of systems with simultaneous cooperation and competition, revealing that their gain distributions are influenced by the Matthew effect and tend to become more heterogeneous over time.

Contribution

It introduces an empirical survey and an analytic model explaining how the Matthew effect drives the evolution of cooperation-competition systems.

Findings

Distribution of gains interpolates between power law and exponential

Longer evolution duration correlates with more heterogeneous gain distribution

Matthew effect amplifies initial heterogeneity regardless of system diversity

Abstract

Systems with simultaneous cooperation and competition among the elements are ubiquitous. In spite of their practical importance, knowledge on the evolution mechanism of this class of complex system is still very limit. In this work, by conducting extensive empirical survey to a large number of cooperation-competition systems which cover wide categories and contain the information of network topology, cooperation-competition gain, and the evolution time, we try to get some insights to the universal mechanism of their evolutions. Empirical investigations show that the distributions of the cooperation-competition gain interpolates between power law function and exponential function. Particularly, we found that the cooperation-competition systems with longer evolution durations tend to have more heterogeneous distributions of the cooperation-competition gain. Such an empirical observation can be well explained by an analytic model in which the evolution of the systems are mainly controlled by the Matthew effect, and the marginal heterogeneity of the initial distribution is amplified by the Matthew effect with similar speed in spite of the diversity of the investigated systems.