IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

Statistical Description of Market Shares in Emergent Market

Listed author(s):
  • 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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: no

Paper provided by University of California at Los Angeles, Center for Computable Economics in its series Working Papers with number _012.

in new window

Date of creation:
Handle: RePEc:wop:callce:_012
Contact details of provider: Postal:
(310) 825 1011

Phone: (310) 825 1011
Fax: (310) 825 9528
Web page:

More information through EDIRC

No references listed on IDEAS
You can help add them by filling out this form.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

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)

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.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.