Economy – Quantitative Finance – General Finance
Scientific paper
2007-12-13
J. Phys. A: Math. Theor. 41 (2008) 185001
Economy
Quantitative Finance
General Finance
9 pages, 1 figure, code and data included with source. Update corrects typos, adds journal-ref
Scientific paper
10.1088/1751-8113/41/18/185001
The rich-get-richer mechanism (agents increase their ``wealth'' randomly at a rate proportional to their holdings) is often invoked to explain the Pareto power-law distribution observed in many physical situations, such as the degree distribution of growing scale free nets. We use two different analytical approaches, as well as numerical simulations, to study the case where the number of agents is fixed and finite (but large), and the rich-get-richer mechanism is invoked a fraction r of the time (the remainder of the time wealth is disbursed by a homogeneous process). At short times, we recover the Pareto law observed for an unbounded number of agents. In later times, the (moving) distribution can be scaled to reveal a phase transition with a Gaussian asymptotic form for r < 1/2 and a Pareto-like tail (on the positive side) and a novel stretched exponential decay (on the negative side) for r > 1/2.
Bagrow James P.
ben-Avraham Daniel
Sun Jie
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