LAUSR

Significance Proportional growth is the driver behind the dynamics of a large class of complex networks. However, if left uncontrolled a few agents may become so dominant that their actions compromise the entire system. We present a framework that monitors the system’s distance from such imbalanced states. When the system approaches an imbalanced state, we show how to structure an optimal, cost-efficient intervention policy. Focusing only on either helping the least-fit agents or punishing the most dominant ones in isolation turns out to be inefficient. Instead, our results call for a more wholistic approach, with important implications for the structure of regulatory matters such as antitrust policies, taxation law, subsidies, or development aid. We develop an early warning system and subsequent optimal intervention policy to avoid the formation of disproportional dominance (“winner takes all,” WTA) in growing complex networks. This is modeled as a system of interacting agents, whereby the rate at which an agent establishes connections to others is proportional to its already existing number of connections and its intrinsic fitness. We derive an exact four-dimensional phase diagram that separates the growing system into two regimes: one where the “fit get richer” and one where, eventually, the WTA. By calibrating the system’s parameters with maximum likelihood, its distance from the unfavorable WTA regime can be monitored in real time. This is demonstrated by applying the theory to the eToro social trading platform where users mimic each other’s trades. If the system state is within or close to the WTA regime, we show how to efficiently control the system back into a more stable state along a geodesic path in the space of fitness distributions. It turns out that the common measure of penalizing the most dominant agents does not solve sustainably the problem of drastic inequity. Instead, interventions that first create a critical mass of high-fitness individuals followed by pushing the relatively low-fitness individuals upward is the best way to avoid swelling inequity and escalating fragility.