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A Finitary Approach To Clustering

In: Industry And Labor Dynamics The Agent-Based Computational Economics Approach

Author

Listed:
  • U. GARIBALDI

    (IMEM-CNR, c/o Department of Physics, University of Genoa, Italy, via Dodecaneso 33, 16146, Genoa, Italy)

  • D. COSTANTINI

    (National Cancer Research Institute (IST), Genoa, Largo Benzi 10, 16132, Genoa, Italy and Department of Statistical Science, University of Bologna, Bologna, Italy)

  • P. VIARENGO

    (National Cancer Research Institute (IST), Genoa, Largo Benzi 10, 16132, Genoa, Italy and Department of Statistical Science, University of Bologna, Bologna, Italy)

Abstract

The clustering of agents in the market is a typical problem dealt with by the new approaches to macroeconomic modeling, that describe macroscopic variables in terms of the behavior of a large collection of microeconomic entities. Clustering has a lot of economical interpretations, that are often described by Ewens’ Sampling Formula (ESF). Contrary to the usual complex derivations, we suggest a finitary characterization of the ESF pointing to real economic processes, Our approach is finitary in the sense that we probabilize a system of n individuals considered as a closed system, a population, where individuals can change attributes as time moves on. The intuitive meaning of the probability is the fraction of time the system spends in the considered partition. As ESF represents an equilibrium distribution satisfying detailed balance, some properties difficult to prove are derived in a simple way. Besides the mean distribution of the cluster sizes, we study the probabilistic time behavior of clusters, in particular the mean survival as a function of the actual size and the correlation between size and age.

Suggested Citation

  • U. Garibaldi & D. Costantini & P. Viarengo, 2004. "A Finitary Approach To Clustering," World Scientific Book Chapters, in: Roberto Leombruni & Matteo Richiardi (ed.), Industry And Labor Dynamics The Agent-Based Computational Economics Approach, chapter 18, pages 377-398, World Scientific Publishing Co. Pte. Ltd..
  • Handle: RePEc:wsi:wschap:9789812702258_0018
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