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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. [ABSTRACT FROM AUTHOR]

The scale-free (SF) property is a major concept in complex networks, and it is based on the definition that an SF network has a degree distribution that follows a power-law (PL) pattern. This paper highlights that not all networks with a PL degree distribution arise through a Barabási−Albert (BA) preferential attachment growth process, a fact that, although evident from the literature, is often overlooked bymany researchers. For this purpose, it is demonstrated, with simulations, that established measures of network topology do not suffice to distinguish between BA networks and other (random-like and latticelike) SF networks with the same degree distribution. Additionally, it is examined whether an existing self-similarity metric proposed for the definition of the SF property is also capable of distinguishing different SF topologies with the same degree distribution. To contribute to this discrimination, this paper introduces a spectral metric, which is shown to be more capable of distinguishing between different SF topologies with the same degree distribution, in comparison with the existing metrics. [ABSTRACT FROM AUTHOR]

Seemingly similar individuals often experience drastically different success trajectories, with some repeatedly failing and others consistently succeeding. One explanation is preexisting variability along unobserved fitness dimensions that is revealed gradually through differential achievement. Alternatively, positive feedback operating on arbitrary initial advantages may increasingly set apart winners from losers, producing runaway inequality. To identify social feedback in human reward systems, we conducted randomized experiments by intervening in live social environments across the domains of funding, status, endorsement, and reputation. In each system we consistently found that early success bestowed upon arbitrarily selected recipients produced significant improvements in subsequent rates of success compared with the control group of nonrecipients. However, success exhibited decreasing marginal returns, with larger initial advantages failing to produce much further differentiation. These findings suggest a lesser degree of vulnerability of reward systems to incidental or fabricated advantages and a more modest role for cumulative advantage in the explanation of social inequality than previously thought. [ABSTRACT FROM AUTHOR]

We develop a model for the distribution of scientific citations. The model involves a dual mechanism: in the direct mechanism, the author of a new paper finds an old paper A and cites it. In the indirect mechanism, the author of a new paper finds an old paper A only via the reference list of a newer intermediary paper B, which has previously cited A. By comparison to citation databases, we find that papers having few citations are cited mainly by the direct mechanism. Papers already having many citations ("classics") are cited mainly by the indirect mechanism. The indirect mechanism gives a power-law tail. The "tipping point" at which a paper becomes a classic is about 25 citations for papers published in the Institute for Scientific Information (ISI) Web of Science database in 1981, 31 for Physical Review D papers published from 1975-1994, and 37 for all publications from a list of high h-index chemists assembled in 2007. The power-law exponent is not universal. Individuals who are highly cited have a systematically smaller exponent than individuals who are less cited. [ABSTRACT FROM AUTHOR]

The relationship between the size and the variance of firm growth rates is known to follow an approximate power-law behavior σ(S) ≈ S[sup-β(S)] where S is the firm size and β(S) ≈ 0.2 is an exponent that weakly depends on S. Here, we show how a model of proportional growth, which treats firms as classes composed of various numbers of units of variable size, can explain this sizevariance dependence. In general, the model predicts that β(S) must exhibit a crossover from β(0) = 0 to β(∞) = 1/2. For a realistic set of parameters, β(S) is approximately constant and can vary from 0.14 to 0.2 depending on the average number of units in the firm. We test the model with a unique industry-specific database in, which firm sales are given in terms of the sum of the sales of all their products. We find that the model is consistent with the empirically observed size-variance relationship. [ABSTRACT FROM AUTHOR]

We introduce a model of proportional growth to explain the distribution Pg(g) of business-firm growth rates. The model predicts that Pg(g) is exponential in the central part and depicts an asymptotic power-law behavior in the tails with an exponent ... = 3. Because of data limitations, previous studies in this field have been focusing exclusively on the Laplace shape of the body of the distribution. In this article, we test the model at different levels of aggregation in the economy, from products to firms to countries, and we find that the predictions of the model agree with empirical growth distributions and size-variance relationships. [ABSTRACT FROM AUTHOR]