# Tripoly Stackelberg game model: One leader versus two followers

Tripoly Stackelberg game model: One leader versus two followers This paper is devoted to introduce and study a Stackelberg game consisting of three competed firms. The three firms are classified as a leader which is the first firm and the other two firms are called the followers. A linear inverse demand function is used. In addition a quadratic cost based on an actual and announced quantities is adopted. Based on bounded rationality, a three-dimensional discrete dynamical system is constructed. For the system, the backward induction is used to solve the system and to get Nash equilibrium. The obtained results are shown that Nash equilibrium is unique and its stability is affected by the system’s parameters by which the system behaves chaotically due to bifurcation and chaos appeared. Some numerical experiments are performed to portrays such chaotic behavior. A control scheme is used to return the system back to its stability state and is supported by some simulations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Computation Elsevier

# Tripoly Stackelberg game model: One leader versus two followers

, Volume 328 – Jul 1, 2018
11 pages

Publisher
Elsevier
ISSN
0096-3003
eISSN
1873-5649
D.O.I.
10.1016/j.amc.2018.01.041
Publisher site
See Article on Publisher Site

### Abstract

This paper is devoted to introduce and study a Stackelberg game consisting of three competed firms. The three firms are classified as a leader which is the first firm and the other two firms are called the followers. A linear inverse demand function is used. In addition a quadratic cost based on an actual and announced quantities is adopted. Based on bounded rationality, a three-dimensional discrete dynamical system is constructed. For the system, the backward induction is used to solve the system and to get Nash equilibrium. The obtained results are shown that Nash equilibrium is unique and its stability is affected by the system’s parameters by which the system behaves chaotically due to bifurcation and chaos appeared. Some numerical experiments are performed to portrays such chaotic behavior. A control scheme is used to return the system back to its stability state and is supported by some simulations.

### Journal

Applied Mathematics and ComputationElsevier

Published: Jul 1, 2018

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just \$49/month

### Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

### Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

### Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

### Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

DeepDyve

DeepDyve

### Pro

Price

FREE

\$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations