Cooperation dynamics in networked geometric Brownian motion

Abstract

Recent works suggest that pooling and sharing may constitute a fundamental mechanism for the evolution of cooperation in well-mixed fluctuating environments. The rationale is that, by reducing the amplitude of fluctuations, pooling and sharing increases the steady-state growth rate at which individuals self-reproduce. However, in reality interactions are seldom realized in a well-mixed structure, and the underlying topology is in general described by a complex network. Motivated by this observation, we investigate the role of the network structure on the cooperative dynamics in fluctuating environments, by developing a model for networked pooling and sharing of resources undergoing a geometric Brownian motion. The study reveals that, while in general cooperation increases the individual steady state growth rates (i.e. is evolutionary advantageous), the interplay with the network structure may yield large discrepancies in the observed individual resource endowments. We comment possible biological and social implications and discuss relations to econophysics.

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“…GBM has been applied in a variety scientific fields [9,[29][30][31][32][33]. Mathematically, it is represented by the Langevin equation…”

“…Geometric Brownian motion (GBM) frequently features in mathematical modeling. The advantage of modelling through this process lies in its universality, as it represents an attractor of more complex models that exhibit non-ergodic dynamics [1][2][3]. As such, GBM has been used to underlie the dynamics of a diverse set of natural phenomena including the distribution of incomes, body weights, rainfall, fragment sizes in rock crushing processes, etc [4,5].…”