Scaling laws of strategic behaviour and size heterogeneity in agent dynamics

The dynamics of many socioeconomic systems is determined by the decision making process of agents. The decision process depends on agent's characteristics, such as preferences, risk aversion, behavioral biases, etc.. In addition, in some systems the size of agents can be highly heterogeneous leading to very different impacts of agents on the system dynamics. The large size of some agents poses challenging problems to agents who want to control their impact, either by forcing the system in a given direction or by hiding their intentionality. Here we consider the financial market as a model system, and we study empirically how agents strategically adjust the properties of large orders in order to meet their preference and minimize their impact. We quantify this strategic behavior by detecting scaling relations of allometric nature between the variables characterizing the trading activity of different institutions. We observe power law distributions in the investment time horizon, in the number of transactions needed to execute a large order and in the traded value exchanged by large institutions and we show that heterogeneity of agents is a key ingredient for the emergence of some aggregate properties characterizing this complex system.Comment: 6 pages, 3 figure

Predicted and Verified Deviations from Zipf's law in Ecology of Competing Products

Zipf's power-law distribution is a generic empirical statistical regularity found in many complex systems. However, rather than universality with a single power-law exponent (equal to 1 for Zipf's law), there are many reported deviations that remain unexplained. A recently developed theory finds that the interplay between (i) one of the most universal ingredients, namely stochastic proportional growth, and (ii) birth and death processes, leads to a generic power-law distribution with an exponent that depends on the characteristics of each ingredient. Here, we report the first complete empirical test of the theory and its application, based on the empirical analysis of the dynamics of market shares in the product market. We estimate directly the average growth rate of market shares and its standard deviation, the birth rates and the "death" (hazard) rate of products. We find that temporal variations and product differences of the observed power-law exponents can be fully captured by the theory with no adjustable parameters. Our results can be generalized to many systems for which the statistical properties revealed by power law exponents are directly linked to the underlying generating mechanism

Statistical Properties of Business Firms Structure and Growth

We analyze a database comprising quarterly sales of 55624 pharmaceutical products commercialized by 3939 pharmaceutical firms in the period 1992--2001. We study the probability density function (PDF) of growth in firms and product sales and find that the width of the PDF of growth decays with the sales as a power law with exponent $\beta = 0.20 \pm 0.01$. We also find that the average sales of products scales with the firm sales as a power law with exponent $\alpha = 0.57 \pm 0.02$. And that the average number products of a firm scales with the firm sales as a power law with exponent $\gamma = 0.42 \pm 0.02$. We compare these findings with the predictions of models proposed till date on growth of business firms

In-plane magnetic reorientation in coupled ferro- and antiferromagnetic thin films

By studying coupled ferro- (FM) and antiferromagnetic (AFM) thin film systems, we obtain an in-plane magnetic reorientation as a function of temperature and FM film thickness. The interlayer exchange coupling causes a uniaxial anisotropy, which may compete with the intrinsic anisotropy of the FM film. Depending on the latter the total in-plane anisotropy of the FM film is either enhanced or reduced. Eventually a change of sign occurs, resulting in an in-plane magnetic reorientation between a collinear and an orthogonal magnetic arrangement of the two subsystems. A canted magnetic arrangement may occur, mediating between these two extremes. By measuring the anisotropy below and above the N\'eel temperature the interlayer exchange coupling can be determined. The calculations have been performed with a Heisenberg-like Hamiltonian by application of a two-spin mean-field theory.Comment: 4 pages, 4 figure

Pareto versus lognormal: a maximum entropy test

It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows one to identify the true data-generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with other widely used methods and applied to different levels of aggregation of complex systems. Our results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units