IDEAS home Printed from
   My bibliography  Save this paper

Optimal Service Speeds in a Competitive Environment


  • Ehud Kalai


This is a study of the economic behavior of vendors of service in competition. A simple model with two competing exponential servers and Poisson arrivals is considered. Each server is free to choose his own service rate at a cost (per time unit) that is strictly convex and increasing. There is a fixed reward to a server for each customer that he serves. The model is designed to study one specific aspect of competition. Namely, competition in speed of service as a means for capturing a larger market share in order to maximize long run expected profit per time unit. A two person strategic game is formulated an its solutions are characterized. Depending on the revenue per customer served and on the cost of maintaining service rates, the following three situations may arise. (i) a unique symmetric strategic (Nash) equilibrium in which expected waiting time is infinite; (ii) a unique symmetric strategic equilibrium in which expected waiting time is finite; and (iii) several, non symmetric strategic equilibria with infinite expected waiting time. An explicit expression for the market share of each server as a function of the service rates of the two servers is also given.

Suggested Citation

  • Ehud Kalai, 1990. "Optimal Service Speeds in a Competitive Environment," Discussion Papers 901, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:901

    Download full text from publisher

    File URL:
    File Function: main text
    Download Restriction: no

    References listed on IDEAS

    1. Colin E. Bell & Shaler Stidham, Jr., 1983. "Individual versus Social Optimization in the Allocation of Customers to Alternative Servers," Management Science, INFORMS, vol. 29(7), pages 831-839, July.
    2. Teghem, J., 1986. "Control of the service process in a queueing system," European Journal of Operational Research, Elsevier, vol. 23(2), pages 141-158, February.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Mei Xue & Patrick T. Harker, 2003. "Service Co-Production, Customer Efficiency and Market Competition," Center for Financial Institutions Working Papers 03-03, Wharton School Center for Financial Institutions, University of Pennsylvania.
    2. Isabel Parra-Frutos, 2010. "A queuing-based model for optimal dimension of service firms," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 1(4), pages 459-474, September.
    3. Pekka Ilmakunnas, 2002. "Strategic behavior in a service industry," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 23(2), pages 69-82.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:nwu:cmsems:901. 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: (Fran Walker). 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.

    If CitEc recognized a reference but did not link an item in RePEc 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 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.