A stochastic multiple-leader Stackelberg model: Analysis, computation, and application

A stochastic multiple-leader Stackelberg model: Analysis, computation, and application

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Article ID: iaor200971639
Country: United States
Volume: 57
Issue: 5
Start Page Number: 1220
End Page Number: 1235
Publication Date: Sep 2009
Journal: Operations Research
Authors: ,
Keywords: game theory
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.

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