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

A stochastic multiple leader Stackelberg model: analysis, computation, and application
A stochastic multiple leader Stackelberg model: analysis, computation, and application
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.
programming, noncooperative games-group decisions, Stackelberg game, equilibrium existence, uniqueness, sample average approximation
0030-364X
1220-1235
DeMiguel, Victor
8c007611-4dd6-4ea3-9832-2be9e532030d
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
DeMiguel, Victor
8c007611-4dd6-4ea3-9832-2be9e532030d
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5

DeMiguel, Victor and Xu, Huifu (2009) A stochastic multiple leader Stackelberg model: analysis, computation, and application. Operations Research, 57 (5), 1220-1235. (doi:10.1287/opre.1080.0686).

Record type: Article

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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More information

Published date: 2009
Keywords: programming, noncooperative games-group decisions, Stackelberg game, equilibrium existence, uniqueness, sample average approximation
Organisations: Operational Research

Identifiers

Local EPrints ID: 79535
URI: http://eprints.soton.ac.uk/id/eprint/79535
ISSN: 0030-364X
PURE UUID: dfb169c0-eec4-47fa-bb01-d2f90d2f96e0
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

Catalogue record

Date deposited: 17 Mar 2010
Last modified: 28 Apr 2022 01:51

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Contributors

Author: Victor DeMiguel
Author: Huifu Xu ORCID iD

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