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

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
avmiguel{at}london.edu
h.xu{at}maths.soton.ac.uk

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.

Subject classifications: programming; noncooperative games/group decisions; Stackelberg game; equilibrium existence; uniqueness; sample average approximation.
History: Received October 2006; revision received February 2008; accepted September 2008.