IDEAS home Printed from
   My bibliography  Save this paper

Statistical Description of Market Shares in Emergent Market


  • Masanao Aoki

    (Center for Computable Economics and Department of Economics, UCLA.)


This paper discusses distributions of the composition of a large number of agents by their types, their choices or some other characteristics such as the market shares of shops when the buyers are classified according to the stores they shop. Models with a large number of types are considered in this paper. We describe the distribution of the order statistics of the fractions of agents as the average of multinomial distributions conditional on the vector of random fractions by Dirichlet distributions for the random fractions. The result is the same as the Ewens formula known in the field of population genetics. The interaction processes of a large number of agents are modeled as Markov processes on the set of exchangeable random partitions of a set of integers. Patterns of composition or shares evolve as random partitions of customers. By introducing some simple transition rates for the types of agents a master equation or a diffusion equation approximation describes the time evolution of the process. We show that the frequency spectrum or intensity of fractions have the same form for the market shares and for the relative sizes of the basins of attractions associated with random maps. The characterization given in this paper of distributions may be useful in designing simulation studies or interpreting results of such studies.

Suggested Citation

  • Masanao Aoki, "undated". "Statistical Description of Market Shares in Emergent Market," Working Papers _012, University of California at Los Angeles, Center for Computable Economics.
  • Handle: RePEc:wop:callce:_012

    Download full text from publisher

    File URL:
    Download Restriction: no


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wop:callce:_012. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Krichel). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.