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A Stochastic Multiple-Leader Stackelberg Model: Analysis, Computation, and Application

Author

Listed:
  • Victor DeMiguel

    (Department of Management Science and Operations, London Business School, Regent's Park, London NW1 4SA, United Kingdom)

  • Huifu Xu

    (School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom)

Abstract

We study an oligopoly consisting of M leaders and N followers that supply a homogeneous product (or service) noncooperatively. Leaders choose their supply levels first, knowing the demand function only in distribution. Followers make their decisions after observing the leader supply levels and the realized demand function. We term the resulting equilibrium a stochastic multiple-leader Stackelberg-Nash-Cournot (SMS) equilibrium. We show the existence and uniqueness of SMS equilibrium under mild assumptions. We also propose a computational approach to find the equilibrium based on the sample average approximation method and analyze its rate of convergence. Finally, we apply this framework to model competition in the telecommunication industry.

Suggested Citation

  • Victor DeMiguel & Huifu Xu, 2009. "A Stochastic Multiple-Leader Stackelberg Model: Analysis, Computation, and Application," Operations Research, INFORMS, vol. 57(5), pages 1220-1235, October.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:5:p:1220-1235
    DOI: 10.1287/opre.1080.0686
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    References listed on IDEAS

    as
    1. Hanif D. Sherali, 1984. "A Multiple Leader Stackelberg Model and Analysis," Operations Research, INFORMS, vol. 32(2), pages 390-404, April.
    2. Hanif D. Sherali & Allen L. Soyster & Frederic H. Murphy, 1983. "Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations," Operations Research, INFORMS, vol. 31(2), pages 253-276, April.
    3. Stephen M. Robinson, 1996. "Analysis of Sample-Path Optimization," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 513-528, August.
    4. Xinmin Hu & Daniel Ralph, 2007. "Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices," Operations Research, INFORMS, vol. 55(5), pages 809-827, October.
    5. Papageorgiou, Nikolaos S., 1985. "On the theory of Banach space valued multifunctions. 1. Integration and conditional expectation," Journal of Multivariate Analysis, Elsevier, vol. 17(2), pages 185-206, October.
    6. D. Ralph & H. Xu, 2005. "Implicit Smoothing and Its Application to Optimization with Piecewise Smooth Equality Constraints1," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 673-699, March.
    7. Daniel Ralph, 1994. "Global Convergence of Damped Newton's Method for Nonsmooth Equations via the Path Search," Mathematics of Operations Research, INFORMS, vol. 19(2), pages 352-389, May.
    8. De Wolf, D. & Smeers, Y., 1997. "A stochastic version of a Stackelberg-Nash-Cournot equilibrium model," LIDAM Reprints CORE 1257, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Daniel De Wolf & Yves Smeers, 1997. "A Stochastic Version of a Stackelberg-Nash-Cournot Equilibrium Model," Management Science, INFORMS, vol. 43(2), pages 190-197, February.
    10. Papageorgiou, Nikolaos S., 1985. "On the theory of Banach space valued multifunctions. 2. Set valued martingales and set valued measures," Journal of Multivariate Analysis, Elsevier, vol. 17(2), pages 207-227, October.
    11. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
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