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Optimal Service Speeds in a Competitive Environment

Author

Listed:
  • Ehud Kalai

    (Department of Managerial Economics and Decision Science, J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60208)

  • Morton I. Kamien

    (Department of Managerial Economics and Decision Science, J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60208)

  • Michael Rubinovitch

    (Faculty of Industrial Engineering and Management, Technion---Israel Institute of Technology, Haifa 32000, Israel)

Abstract

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 and 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, nonsymmetric 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 & Morton I. Kamien & Michael Rubinovitch, 1992. "Optimal Service Speeds in a Competitive Environment," Management Science, INFORMS, vol. 38(8), pages 1154-1163, August.
    • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:8:p:1154-1163
    DOI: 10.1287/mnsc.38.8.1154
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    References listed on IDEAS

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    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.
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