Prosperity is associated with instability in dynamical networks

TL;DR

This paper demonstrates that in dynamic social, biological, and economic networks, cooperation fosters prosperity but also leads to instability through cycles of network formation and fragmentation driven by imitation and internal conflicts.

Contribution

It introduces a game-theoretic model showing how simple imitation and conflicts between cooperators and defectors cause cycles of network prosperity and instability.

Findings

Cooperators promote highly connected prosperous networks.

Defectors cause network fragmentation and decline.

Prosperity is linked to frequent network formation and fragmentation.

Abstract

Social, biological and economic networks grow and decline with occasional fragmentation and re-formation, often explained in terms of external perturbations. We show that these phenomena can be a direct consequence of simple imitation and internal conflicts between 'cooperators' and 'defectors'. We employ a game-theoretic model of dynamic network formation where successful individuals are more likely to be imitated by newcomers who adopt their strategies and copy their social network. We find that, despite using the same mechanism, cooperators promote well-connected highly prosperous networks and defectors cause the network to fragment and lose its prosperity; defectors are unable to maintain the highly connected networks they invade. Once the network is fragmented it can be reconstructed by a new invasion of cooperators, leading to the cycle of formation and fragmentation seen, for example, in bacterial communities and socio-economic networks. In this endless struggle between cooperators and defectors we observe that cooperation leads to prosperity, but prosperity is associated with instability. Cooperation is prosperous when the network has frequent formation and fragmentation.