Success-breeds-success distributional dynamics in stochastic competitive systems

Simon (Biometrika 52:425–440, 1955) demonstrated that distributional principles are not necessarily field-specific. Several investigations across various disciplines have referred to similar types of power-law distributions, which inherently incline towards the concentration of the outcome variable. These patterns are often attributed to the so-called “success-breeds-success” (SBS) principle. The first aim of this paper is to decipher the fundamentals of this principle across various disciplines. The second aim is to create a supra-disciplinary model that is able to serve as a default analytical tool for the modelling of SBS dynamics within competitive stochastic systems, for the purpose of which we position homogeneous agents with self-preserving behaviour in competition for scarce resources. It is given that: (1) Agents are not auto-reproductive; hence the self-preservation stimulus forces them to appropriate resources; (2) appropriable resources exist in limited quantities at a given time and in a given space, and agents must compete for these scarce resources; (3) agents implicitly pursue their competitiveness in order to appropriate enough resources for their lifelong reproduction; and (4) the more resources the agent has in the present, the higher the probability of his appropriation in the future. Assuming these conditions, we ran a simulation of 25 million mutual interactions based on the binary dyadic tree for two-agent competition. Despite the perfectly competitive market conditions, the results revealed diverging accumulation trajectories. In contrast to mainstream economic models, the paper provides new perspectives on competition and suggests, in particular, that the distributional dynamics of competitive markets comprise the inequality-driving force in market economies.