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

Authors:
Victor DeMiguel;Huifu Xu
Affiliations:
Department of Management Science and Operations, London Business School, Regent's Park, London NW1 4SA, United Kingdom;School of Mathematics, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
Venue:
Operations Research
Year:
2009

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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.