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Pricing problems with a continuum of customers as stochastic Stackelberg games

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Abstract

The pricing problem where a company sells a certain kind of product to a continuum of customers is considered. It is formulated as a stochastic Stackelberg game with nonnested information structure. The inducible region concept, recently developed for deterministic Stackelberg games, is extended to treat the stochastic pricing problem. Necessary and sufficient conditions for a pricing scheme to be optimal are derived, and the pricing problem is solved by first delineating its inducible region, and then solving a constrained optimal control problem.

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Author information

Authors and Affiliations

  1. Department of Electrical and Systems Engineering, University of Connecticut, Storrs, Connecticut

    P. B. Luh (Associate Professor)

  2. Department of Electrical and Computer Engineering, University of California, Davis, California

    T. S. Chang (Assistant Professor)

  3. Department of Electrical and Computer Engineering, Trinity College, Hartford, Connecticut

    T. Ning (Assistant Professor)

Authors
  1. P. B. Luh
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  2. T. S. Chang
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  3. T. Ning
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Additional information

Communicated by J. B. Cruz, Jr.

The research work reported here as supported in part by the National Science Foundation under Grant ECS-81-05984, Grant ECS-82-10673, and by the Air Force Office of Scientific Research under AFOSR Grant 80-0098.

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Luh, P.B., Chang, T.S. & Ning, T. Pricing problems with a continuum of customers as stochastic Stackelberg games. J Optim Theory Appl 55, 119–131 (1987). https://doi.org/10.1007/BF00939048

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