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arXiv · 1706.04190

How the fittest compete for leadership: A tale of tails

J. M. Luck·A. Mehta
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Abstract

We investigate how leaders emerge as a consequence of the competitive dynamics between coupled papers in a model citation network. Every paper is allocated an initial fitness depending on its intrinsic quality. Its fitness then evolves dynamically as a consequence of the competition between itself and all the other papers in the field. It picks up citations as a result of this adaptive dynamics, becoming a leader if it has the highest citation count at a given time. Extensive analytical and numerical investigations of this model suggest the existence of a universal phase diagram, divided into regions of weak and strong coupling. In the former, we find an `extended' and rather structureless distribution of citation counts among many fit papers; leaders are not necessarily those with the maximal fitness at any given time. By contrast, the strong-coupling region is characterised by a strongly hierarchical distribution of citation counts, that are `localised' among only a few extremely fit papers, and exhibit strong history-to-history fluctuations, as a result of the complex dynamics among papers in the tail of the fitness distribution.

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J. M. Luck, A. Mehta. 2017-06-26. How the fittest compete for leadership: A tale of tails. https://doi.org/10.1103/physreve.95.062306

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