Competition in Social Networks: Emergence of a Scale-free Leadership Structure and Collective Efficiency

TL;DR

This paper models competition in social networks using a minority game framework, revealing how communication fosters a scale-free leadership structure and enhances collective efficiency.

Contribution

It introduces a coupled influence network that develops a scale-free leadership structure and demonstrates how communication improves cooperation among agents.

Findings

Influence network develops scale-free hubs.

Communication leads to high cooperation levels.

System achieves near-maximal efficiency.

Abstract

Using the minority game as a model for competition dynamics, we investigate the effects of inter-agent communications on the global evolution of the dynamics of a society characterized by competition for limited resources. The agents communicate across a social network with small-world character that forms the static substrate of a second network, the influence network, which is dynamically coupled to the evolution of the game. The influence network is a directed network, defined by the inter-agent communication links on the substrate along which communicated information is acted upon. We show that the influence network spontaneously develops hubs with a broad distribution of in-degrees, defining a robust leadership structure that is scale-free. Furthermore, in realistic parameter ranges, facilitated by information exchange on the network, agents can generate a high degree of cooperation making the collective almost maximally efficient.