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

Journal

Operations Research

Subject

Management Science and Operations

Publishing details

Operations Research 2009 Vol 57:5 p 1220-1235

Authors / Editors

DeMiguel V;Xu H

Biographies

Victor DeMiguel

Publication Year

2009

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.

Keywords

Programming; Noncooperative games/group decisions; Stackelberg game; Equilibrium existence; Uniqueness; Sample average approximation

Available on ECCH

No


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