Complex dynamics analysis for a Bertrand duopoly model with bounded rationality

Ji Xiang Zhang; De Qun Zhou; Yan Hua Wang

doi:10.1109/ICMSE.2009.5317513

Complex dynamics analysis for a Bertrand duopoly model with bounded rationality

Ji Xiang Zhang^*, De Qun Zhou, Yan Hua Wang

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Citations (Scopus)

Abstract

A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.

Original language	English
Title of host publication	2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009
Pages	190-195
Number of pages	6
DOIs	https://doi.org/10.1109/ICMSE.2009.5317513
Publication status	Published - 2009
Externally published	Yes
Event	2009 16th International Conference on Management Science and Engineering, ICMSE 2009 - Moscow, Russian Federation Duration: 14 Sept 2009 → 16 Sept 2009

Publication series

Name	2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009

Conference

Conference	2009 16th International Conference on Management Science and Engineering, ICMSE 2009
Country/Territory	Russian Federation
City	Moscow
Period	14/09/09 → 16/09/09

Keywords

Bertrand duopoly model
Discrete dynamical system
Heterogeneous expectations
Nash equilibrium
Stability

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10.1109/ICMSE.2009.5317513

Cite this

Zhang, J. X., Zhou, D. Q., & Wang, Y. H. (2009). Complex dynamics analysis for a Bertrand duopoly model with bounded rationality. In 2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009 (pp. 190-195). Article 5317513 (2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009). https://doi.org/10.1109/ICMSE.2009.5317513

Zhang, Ji Xiang ; Zhou, De Qun ; Wang, Yan Hua. / Complex dynamics analysis for a Bertrand duopoly model with bounded rationality. 2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009. 2009. pp. 190-195 (2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009).

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title = "Complex dynamics analysis for a Bertrand duopoly model with bounded rationality",

abstract = "A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.",

keywords = "Bertrand duopoly model, Discrete dynamical system, Heterogeneous expectations, Nash equilibrium, Stability",

author = "Zhang, {Ji Xiang} and Zhou, {De Qun} and Wang, {Yan Hua}",

year = "2009",

doi = "10.1109/ICMSE.2009.5317513",

language = "English",

isbn = "9781424439706",

series = "2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009",

pages = "190--195",

booktitle = "2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009",

note = "2009 16th International Conference on Management Science and Engineering, ICMSE 2009 ; Conference date: 14-09-2009 Through 16-09-2009",

}

Zhang, JX, Zhou, DQ & Wang, YH 2009, Complex dynamics analysis for a Bertrand duopoly model with bounded rationality. in 2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009., 5317513, 2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009, pp. 190-195, 2009 16th International Conference on Management Science and Engineering, ICMSE 2009, Moscow, Russian Federation, 14/09/09. https://doi.org/10.1109/ICMSE.2009.5317513

Complex dynamics analysis for a Bertrand duopoly model with bounded rationality. / Zhang, Ji Xiang; Zhou, De Qun; Wang, Yan Hua.
2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009. 2009. p. 190-195 5317513 (2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.

KW - Bertrand duopoly model

KW - Discrete dynamical system

KW - Heterogeneous expectations

KW - Nash equilibrium

KW - Stability

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Zhang JX, Zhou DQ, Wang YH. Complex dynamics analysis for a Bertrand duopoly model with bounded rationality. In 2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009. 2009. p. 190-195. 5317513. (2009 International Conference on Management Science and Engineering - 16th Annual Conference Proceedings, ICMSE 2009). doi: 10.1109/ICMSE.2009.5317513

Complex dynamics analysis for a Bertrand duopoly model with bounded rationality

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